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61 Mathematics and Science Education ABS-125

Business Statistics Competence to Support Work-Skill Courses of Diploma 4 Non-Engineering Study Program of Politeknik Negeri Bandung in the 21st Century
Neneng Nuryati, Siti Syamsiyah Purwaningsih, Ira Novianty, Tjetjep Djuwarsa, Neneng Dahtiah, Djoni Djatnika , Carolina M Lasambouw, Anny Suryani, Endang Habinuddin, Amar Sumarsa

Politeknik Negeri Bandung


Abstract

The Study program of Government Management Accounting (AMP) is a non-engineering program with the vision to prepare graduates with entrepreneurial spirit and environmentally sound and moral. Graduate competency is indispensable in the development and advancement of technology in the 21st century. The graduate competency fulfillment is by providing them with the applicable knowledge such as applied statistics. It is one of the compulsory courses that contains ways to collect, present, analyze, and conclude data obtained in the form of decisions. One of the challenges in delivering this course is the level differences on students^ statistical literacy abilities. This research aims to evaluate the role of a business statistics course in the work-skill courses of non-engineering study programs in Politeknik Negeri Bandung. This research applied quantitative research with a descriptive correlation method. The finding shows that there is a positive relationship between the statistics course and non-engineering courses in the AMP study program, which is 0.507. The data shows a positive correlation between the statistics course and non-engineering courses in the AMP study program as shown by the regression equation Y &#770-= 2.675 + 0.227X. The magnitude of the contribution of this course to the increase in non-engineering courses in the AMP study program is indicated by the coefficient of determination of 0.257. This shows 25.7% of the statistics course make a positive contribution to non-engineering courses in the AMP study program while the rest is influenced by other factors outside the course.

Keywords: Business Statistics Competence- Support Work-Skill Courses of Diploma 4 Non-Engineering

Share Link | Plain Format | Corresponding Author (Neneng Nuryati)


62 Mathematics and Science Education ABS-136

Implementation of the Merdeka Curriculum in Mathematics Learning at SMP Negeri 3 Sukoharjo in the Academic Year 2022/2023
Zulfa Izzana

Universitas Sebelas Maret


Abstract

This qualitative descriptive research aims to explore the implementation of the Merdeka Curriculum in mathematics education at SMP Negeri 3 Sukoharjo. The study involved key informants, including school authorities, mathematics teachers, and seventh-grade students, and utilized documents like teaching modules and assessments. Purposive sampling was employed for data collection through observations, interviews, questionnaires, and document analysis, ensuring data validity via method and source triangulation. Interactive analysis techniques were used for data analysis.

The findings revealed that teachers demonstrated a strong grasp of the Merdeka Curriculum^s learning outcomes, making necessary adjustments to provided teaching modules. While student-centered approaches were attempted, further refinements were required in their teaching practices. Periodic formative assessments were conducted, aiding in identifying students needing extra attention. Challenges faced included limited teacher knowledge about the curriculum, the need for implementation adjustments, inadequate facilities, difficulties in student-centered and differentiated learning, lack of curiosity, and monotonous teaching methods.

To address these challenges, efforts included regular teacher training, supervision, and evaluation, as well as enhancing facilities and infrastructure. Relevant assessments were developed, and teacher collaboration was promoted. Stimulus and motivation were provided to students, fostering a collaborative learning environment, and open communication between students and teachers was encouraged. These concerted efforts aimed to enhance the effectiveness of the Merdeka Curriculum implementation, ultimately improving mathematics education at SMP Negeri 3 Sukoharjo.

Keywords: implementation of the Merdeka Curriculum, formative assessments, differentiated teaching

Share Link | Plain Format | Corresponding Author (Zulfa Izzana)


63 Mathematics and Science Education ABS-137

DEVELOPMENT OF LEARNING TRAJECTORY OF GRADE VII SMP STUDENTS ON PRISM VOLUME MATERIAL IN PROBLEM BASED LEARNING
Luthfi Almira , Budi Usodo, Yemi Kuswardi*

Sebelas Maret University


Abstract

This research aimed to produce a learning trajectory on prism volume material in problembased learning. The type of research used is design research with three stages: (1) preparing for the experiment, (2) design experiment, and (3) retrospective analysis. The research subjects were students of class VII in 2 Wonogiri junior high schools. The trial of hypothetical Learning Trajectory (HLT) for cycle 1 or so called pilot experiment involved 6 students of class VII E and trial of HLT for cycle 2 or so called teaching experiment involved 32 students of class VII G. The instruments for data collection were observation sheet, interview protocol, and learning video recording. The prism volume learning trajectory started from definition of the prism, determining the elements of prism, grouping examples and non-examples of prism, and finding the formula for the volume of prism. The research obtained that the learning trajectory can contribute to assist students in finding and developing an understanding of the concept of prism
volume formula.

Keywords: learning trajectory, problem-based learning, prism volume

Share Link | Plain Format | Corresponding Author (Yemi Kuswardi)


64 Mathematics and Science Education ABS-138

MOTION COMIC INTERACTIVE VIDEO FOR MATHEMATICAL LITERACY IN ELEMENTARY SCHOOL
Farida Nurhasanah, Matias Vico Anggoro Kristanto, Henny Ekana Chrisnawati

Prodi Pendidikan Matematika, Fakultas Keguruan dan Ilmu Pendidikan, Univrsitas Sebelas Maret


Abstract

This research aims to develop a valid, practical, and effective interactive video motion comic based on story-based learning to teach algebra concepts to elementary school students. The media development model employed in this study is the ADDIE model (Analysis, Design, Development, Implementation, Evaluation). During the analysis phase, data was gathered through tests, interviews, and literature review to assess students^ performance, abilities, facts, concepts, procedures, and learning objectives. A quasi-experimental study was conducted to determine whether the developed video could enhance students^ literacy in algebra. The findings revealed that students were engaged when teachers used storytelling as an explanatory method. However, some students faced difficulties in understanding story-based math problems due to their limited experiences with this approach. In the design phase, the video concept was developed to address the identified issues. This involved selecting motion comic animation as the appropriate format, predominantly using animal characters, structuring the storyline, organizing algebraic content, and scripting the video. The development stage involved creating the interactive video motion comic using Adobe After Effects and Adobe Premiere Pro. During the implementation phase, the video motion comic based on story-based learning for algebra was tested in first and third-grade classes. The evaluation process comprised expert validation, user feedback on practicality, and an assessment of the media^s effectiveness. The results of the research indicate that the developed media was deemed valid for enhancing students^ mathematical literacy skills, and it was considered practical for teaching algebra in elementary schools, based on the Gain test. These outcomes suggest that the interactive video motion comic based on story-based learning for algebra holds promise for further experimentation with longer study duration.

Keywords: mathematical literacy, motion comic, interactive video, story based learning, aljabar

Share Link | Plain Format | Corresponding Author (Farida Nurhasanah)


65 Mathematics and Statistics ABS-1

Stunting Modeling Using Robust Regression: Maximum Likelihood, Method of Moment, and Generalized Maximum Likelihood Estimations
Yuliana Susanti, Hasih Pratiwi, Respatiwulan, Sri Sulistijowati Handajani, Muhammad Bayu Nirwana, Ilmia Hamidah

Universitas Sebelas Maret, Surakarta, Indonesia


Abstract

Stunting is a serious health problem facing the world. Stunting results from chronic or recurrent undernutrition, usually associated with poverty, poor maternal health and nutrition, frequent illness, and inappropriate early feeding and care in early life. According to WHO, in 2019, the global prevalence of stunting reached 29.9%, and Asia was in second place with a percentage of 31.9%. In 2021, the stunting rate in Indonesia was 24.4%, which is above the WHO standard of 20%. Factors that are thought to affect stunting are iron supplement tablets, exclusive breastfeeding, proper sanitation facilities, and toddlers suffering from diarrhea. One method to analyze the factors that influence stunting is robust regression. Robust regression is a method used when there are some outlier data or, the data is not normally distributed. This research aims to develop a robust regression model for the number of stunting in Indonesia based on the influencing factors. Several estimation methods that can use in robust regression are maximum likelihood (M) estimation, method of moment (MM), and generalized M (GM) estimation. The results showed that the model with GM estimation was the best because it had the largest adjusted R squared and the smallest AIC. Partial tests showed that all independent variables significantly affect the number of stunting in Indonesia.

Keywords: stunting, robust regression, M estimation, MM estimation, GM estimation

Share Link | Plain Format | Corresponding Author (Yuliana Susanti)


66 Mathematics and Statistics ABS-6

Parameters Estimation and Model Hypotesis Testing On Bivariate Zero-Inflated Negative Binomial Regression
Rahmania Azwarini (a*), Purhadi (a**), Achmad Choiruddin (a)

a) Department of Statistics, Faculty of Science and Data
Analytics, Institut Teknologi Sepuluh Nopember, Arief Rahman Hakim Street, Surabaya 60111, Indonesia.
*rahmaniaazwarini[at]gmail.com
**purhadi[at]statistika.its.ac.id


Abstract

Poisson regression is a regression model that commonly used to model count data. Unfortunately, the Poisson regression modelling on the count data can be failed, which can be caused by overdispersion. Overdispersion is a condition when the variance value is greater than the mean value in the data. Overdispersion can be caused by two aspects, namely overdispersion due to unobserved sources of diversity in the data and overdispersion due to excess zeros in the data. Therefore, this research developed a model that can handle issues that cause overdispersion especially at bivariate count data, namely Bivariate Zero-Inflated Negative Binomial (BZINBR). BZINBR model has the advantages that it does not require the same variance values as the average value, and there is dispersion parameter to describe the variation of the data. BZINBR model can be applied to count data that consist of two response variables. This research focuses on the development of BZINBR type II to deal with overdispersion issues, where the BZINBR type II model has response variables that consists of several combinations pairs of Y values. This study also proposes an efficient algorithm for parameter estimation using the Maximum Likelihood Estimation (MLE) method followed by Berndt-Hall-Hall- Hausman (BHHH) iterations and testing hypotheses using the Maximum Likelihood Ratio Test (MLRT) method. The results of this study are expected to be source of new knowledge for readers in statistical science, particularly related to the BZINBR model.

Keywords: Bivariate Zero-Inflated Negative Binomial- BHHH- MLE- MLRT- Overdispersion

Share Link | Plain Format | Corresponding Author (RAHMANIA AZWARINI)


67 Mathematics and Statistics ABS-7

Dynamic Factor Model Applications Based on Google Trends and Macroeconomic Data for Nowcasting the Gross Domestic Growth of Indonesia
Restu Sri Rahayu(a), Irhamah(a*), Kartika Fithriasari(a)

a) Department of Statistics, Faculty of Science and Data Analytics, Institut Teknologi Sepuluh Nopember, Kampus ITS-Sukolilo, Surabaya, 60111, Indonesia
*irhamah[at]statistika.its.ac.id


Abstract

Dynamic Factor Model (DFM) is a development of time series analysis that is used to perform near-range nowcasting. This model can relate the monthly frequency of the predictor variable to the quarterly frequency of the response variable. DFM has been widely used in economic fields because it can relate economic variables observed in different periods. The availability of economic data, which tends to experience delays, is one of the problems that are commonly encountered. In general, formulating economic policies requires information on economic conditions that is readily available. Policymakers need to know the current economic conditions as a foundation or a basis for projecting future economic conditions. However, macroeconomic indicators tend to be released and available with a long delay. Furthermore,the economic condition of a country can be reflected in the GDP of country. The growth of GDP plays a very important role in helping policymakers and business society understand economic conditions of the country. GDP data has been delayed in its release for five weeks since the quarter ended. This condition occurs at the national levels. Therefore, this study aims to nowcast the growth of GDP in Indonesia using official statistics and google trends data using the DFM.

Keywords: Dynamic Factor Model (DFM), nowcasting, google trends

Share Link | Plain Format | Corresponding Author (Restu Sri Rahayu)


68 Mathematics and Statistics ABS-8

Forecasting Indonesia^s Export Value using The Hybrid Method of ARIMAX-FFNN and Extreme Gradient Boosting (XGBoost)
Andra Citta Passadhi Arya, Heri Kuswanto, Kartika Fithriasari

Department of Statistics, Institut Teknologi Sepuluh Nopember (ITS), Sukolilo, Surabaya, 60111, Indonesia


Abstract

Accurate forecasting of Indonesia^s export value has an important urgency as a reference for formulating national economic growth targets. The value of Indonesia^s exports is believed to be influenced by various external factors, including the exchange rate of the rupiah and import values. Therefore, it is important to model the forecast of Indonesia^s export value by incorporating these factors. The forecasting method used is a hybrid approach that combines two models, a linear and a nonlinear model, with the aim of producing more accurate predictions. The first stage involves linear modeling using the Autoregressive Integrated Moving Average with Exogenous Variables (ARIMAX) model. Subsequently, in the second stage, hybrid modeling is conducted by utilizing the residual input from the linear model and employing a machine learning approach known as the Feed Forward Neural Network (FFNN) to capture nonlinear patterns. In addition to the hybrid modeling, another machine learning algorithm, Extreme Gradient Boosting (XGBoost), is also employed. The aim of this research is to compare the accuracy of the hybrid ARIMAX-FFNN and XGBoost forecasting models. By doing so, it aims to determine which model performs better in terms of accuracy. The selection of the best model is based on the smallest values of Root Mean Square Error (RMSE) and Mean Absolute Percentage Error (MAPE).

Keywords: Forecasting, Export, ARIMAX-FFNN, XGBoost

Share Link | Plain Format | Corresponding Author (Andra Citta Passadhi Arya)


69 Mathematics and Statistics ABS-9

Multivariate Adaptive Inverse Gaussian Regression Spline Modeling for Estimation of Household per Capita Expenditure
Ifah Durrotun Nisa (a), Bambang Widjanarko Otok (a*), Sutikno (a)

a) Departement of Statistics, Faculty of Science and Data Analytics, Institut Teknologi Sepuluh Nopember, Surabaya, 60111, Indonesia
*dr.otok.bw[at]gmail.com


Abstract

Multivariate Adaptive Regression Spline (MARS) is used for high-dimensional data modeling. It is able to allow the additive and interactions effects among predictor variables. For continuous responses variable, sometimes, the data has highly skewness to right. An alternative method that can handle it is inverse Gaussian regression (IGR). Multivariate Adaptive Inverse Gaussian Regression Spline (MAIGRS) model is a combination of MARS and IGR. In this modeling, the estimation of basis function parameters obtained by Weighted Least Square (WLS) method. In this study, MAIGRS model is applied for prediction household per capita expenditure. Secondary data from the Pohuwato Regency National Socioeconomic Survey (SUSENAS) for 2020-2021 was used with an observation unit of 1061 households. There are nineteen predictor variables used in the modeling. The result show that demographic composition, housing conditions, and household asset ownership have a role in predicting household expenditure. Four variables that have a major role in predicting household per capita expenditure are car ownership, percentage of paid worker of household members, percentage of household members with high school education and above, and type of floor, which variable importance level more than 75 percent.

Keywords: Expenditure- IGR- MAIGRS- MARS- WLS

Share Link | Plain Format | Corresponding Author (Ifah Durrotun Nisa)


70 Mathematics and Statistics ABS-10

Modeling Elementary School Dropout in East Java Province Using Binary Logistic Regression
Khomaria Nurul Ainy, Dedy Dwi Prastyo, Ismaini Zain

Department of Statistics, Institut Teknologi Sepuluh Nopember, Kampus ITS-Sukolilo, Surabaya 60111, Indonesia


Abstract

The primary school dropout in 2022 is 38,716 children, and East Java Province contributes 6.37% to the dropout rate at the national level. The problem of dropping out of school is a serious problem considering that the Law on the Indonesian National Education System states that every citizen aged seven to fifteen is required to attend basic education. The main objective of this study is to find out the factors that influence elementary school dropouts in East Java with dichotomous categorical response variables using binary logistic regression analysis. The data used in this research were 1,048,575 students consisting of 1 response variable and 10 predictor variable. The results of the study indicate that based on the analysis performed, the variable that has a significant effect on elementary school dropouts in East Java Province, Indonesia is the level of class (X2), age (X3), distance from home to school (X5), number of siblings (X6), repeat status (X7), parent^s job (X9), and parent^s income (X10). The results of this study can be used as a reference for dealing with the problem of dropping out of school, especially on the factors that have a significant effect on dropping out of school.

Keywords: elementary school dropouts- east java- binary logistic regression

Share Link | Plain Format | Corresponding Author (Khomaria Nurul Ainy)


71 Mathematics and Statistics ABS-13

Dynamic Factor Model to Nowcasting the Sectoral Economic Growth Using High-Frequency Data
Putu Krishnanda Supriyatna, Dedy Dwi Prastyo, Muhammad Sjahid Akbar

Institut Teknologi Sepuluh Nopember


Abstract

Economic growth is an important indicator used for evaluation and planning by many users. Unfortunately, the release of economic growth data has a delay of more than a month. A delay in the availability of economic indicators will impact unpreparedness in dealing with an economic condition. On the other hand, the timely availability of economic indicators can optimize their use in evaluating the economic situation. The nowcasting method is a solution to get an overview of economic conditions more quickly and in near real-time. To provide information quickly, other indicators are needed as proxy components that can be obtained in real-time using high-frequency data. The predictive power of high-frequency data is better because it contains more information. Moreover, economic growth data are only available quarterly. Therefore, such information will be missing if the high-frequency variables used as proxy components are transformed into quarterly data. Therefore, a method is needed to overcome these issues. One method that can be utilized to solve this problem is the DFM (Dynamic Factor Model), which can perform nowcasting using high-frequency data. The predictors used in this nowcasting approach are indicators with a short time lag so that it can provide a quick estimation. Also, forecasting will be carried out in this study using the ARIMAX (Autoregressive Integrated Moving Average with Endogenous Variables) method to see the impact of high-frequency data, with the monthly variables will be transformed into quarterly in the ARIMAX method. The nowcasting results between the DFM and ARIMAX methods will be compared to conclude which method performs better. In addition, the same procedure will be applied to nowcasting the economic growth at the sectoral level.

Keywords: ARIMAX, DFM, High-Frequency Data, Sectoral GDP, Nowcasting Sectoral Economic Growth

Share Link | Plain Format | Corresponding Author (Putu Krishnanda)


72 Mathematics and Statistics ABS-17

Nowcasting Population using Support Vector Regression (SVR) and Multi-Output Support Vector Regression (M-SVR)
Riyan Zulmaniar Vinahari (a*,b), Hidayatul Khusna (a), Heri Kuswanto (a)

a) Department of Statistics, Institut Teknologi Sepuluh Nopember, Kampus ITS - Sukolilo, Surabaya 60111, Indonesia
*riyanzv[at]bps.go.id
b) Badan Pusat Statistik Kabupaten Kendal, Kendal 51351, Indonesia


Abstract

Abstract. DKI Jakarta, West Java, Central Java, and East Java population on a yearly basis is an important data for planning and evaluation in medium- and long-term national development. These data cannot be provided through the population registration system. In addition, Badan Pusat Statistik (BPS-Statistics Indonesia) only provides the population data on a regular basis for each five-year period. Therefore, the population projection is required to provide the total population on a yearly basis. The common method used in population projection is the cohort component method (CCM). CCM is widely used in many countries, including Indonesia. BPS, as an official government institution in Indonesia, also uses CCM to estimate the Indonesian population. Unfortunately, this method has several drawbacks with less accuracy, and therefore, a more accurate method is required. One of the promising methods is nowcasting, which predicts the current value based on a variety of socioeconomic and macroeconomic variables with high frequency data over a yearly period. Due to technological advancements, time series analysis can now be conducted not only using classical statistical methods but also machine learning (ML). In this work, machine learning with a two different nowcasting methods were evaluated. Support Vector Regression (SVR) and Multi-output Support Vector Regression (MSVR) were applied and compared to predict yearly population nowcasts in DKI Jakarta, West Java, Central Java, and East Java Province. The performance comparison between SVR and MSVR is evaluated based on the Root Mean Square Error (RMSE) and Mean Absolute Percentage Error (MAPE). The data used in this work were obtained from BPS, with the output variable being the population of several provinces on Java Island, such as DKI Jakarta, West Java, Central Java, and East Java. The results show that based on the simulation, MSVR outperforms SVR, as shown by a smaller RMSE and MAPE. This indicates that MSVR can be a powerful machine learning-based nowcasting method to be used in population projection in DKI Jakarta, West Java, Central Java, and East Java.

Keywords: Machine Learning, Multioutput Support Vector Regression, Nowcasting, Population, Support Vector Regression

Share Link | Plain Format | Corresponding Author (Riyan Zulmaniar Vinahari)


73 Mathematics and Statistics ABS-18

Random Effects Meta Regression on the Effectiveness of Acceptance and Commitment Therapy for Depression
Felinda Arumningtyas (a), Bambang Widjanarko Otok (a*), Santi Wulan Purnami (a)

a) Faculty of Science and Data Analytics, Institut Teknologi Sepuluh Nopember, Kampus ITS-Sukolilo, 60111 Surabaya
*dr.otok.bw[at]gmail.com


Abstract

Meta-analysis is a statistical technique for summarising the results of two or more similar studies into a blend of quantitative data. Heterogeneity between studies often occurs in meta-analysis. Meta-regression is an extension of meta-analysis that can explain heterogeneity among the results of multiple studies can be attributed to one or more study characteristics. The model in meta-regression that involves variance between studies is the random effects model. The purpose of this study is to apply the random effects meta-regression model. Estimation of model parameters in random effects meta regression uses the Weighted Least Square (WLS) method and for variance estimation is done using the DerSimonian & Laird approach. The data used as research units were 33 published studies that discussed the effectiveness of Acceptance and Commitment Therapy (ACT) in reducing depression levels collected from PubMed, Google Scholar, and Science Direct databases. A combined effect size of -0.321 was obtained, indicating that ACT can reduce depression levels as seen from the decrease in depression levels of the experimental group when compared to the control group. The heterogeneity obtained is 92.58% which indicates high heterogeneity and must be traced, the results of meta regression show that the variables of average patient age and length of therapy sessions can explain the heterogeneity between effect size.

Keywords: ACT- Depression- Meta Analysis- Meta Regression- Weighted Least Squares

Share Link | Plain Format | Corresponding Author (Felinda Arumningtyas)


74 Mathematics and Statistics ABS-19

Counting Process Approach with Frailty on Recurrence Data of Chronic Kindey Disease Patients Using Hu-Care Therapy at Nur Hidayah Hospital Bantul
Insani Hasanah (a), Santi Wulan Purnami (a*), Sagiran (b)

a) Department of Statistics, Faculty of Science and Data Analytics, Institut Teknologi Sepuluh Nopember, Surabaya 60111, Indonesia
*santi_wp[at]statistika.its.ac.id
b) Department of Medicine, Faculty of Medicine and Health Science, Universitas Muhammadiyah Yogyakarta, Yogyakarta 55183, Indonesia


Abstract

Survival analysis is a statistical method used to analyze time data until events occur. This method is used to study the factors that influence the time of occurrence of events or so-called events. In survival analysis, generally only one major event is monitored, such as patient death or equipment failure. However, sometimes in research it can also occur that more than one event is observed, as in the case of patients with chronic illnesses who can experience various events such as curing an illness or being hospitalized repeatedly. Survival analysis with repeated events is used to analyze the time between each event that occurs in each subject or observation. In survival analysis, there are two types of approaches that can be used for recurring data, including the counting process approach and the stratified cox approach. In the case of repeated hospitalizations, it is assumed that each individual has the same/identical factors for repeated hospitalizations, so in this case the counting process approach is used. However, in reality every individual has risk factors that are unobserved and difficult to measure. Based on this, there is a model that takes into account factors that are difficult to measure or not observed in an event which is commonly referred to as the frailty model. The frailty factor can be interpreted as an individual factor that is not observable and influences the individual^s tendency to experience recurring events. Thus, the purpose of this study is to analyze the data on repeated events using the frailty counting process approach. The data used in this study were chronic kidney failure inpatients receiving hu-care therapy at Nur Hidayah Hospital, Bantul. In statistical analysis, chronic kidney disease patients can be considered as a recurring event because there are several factors such as medical complications or hemodialysis which are a cause for patients to experience several hospitalizations over a certain period of time.

Keywords: Chronic Kidney Disease, Counting Process Approach, Frailty, Hu-Care Therapy, Recurrence

Share Link | Plain Format | Corresponding Author (Insani Hasanah)


75 Mathematics and Statistics ABS-20

Prediction-Oriented Segmentation Partial Least Square (POS-PLS) in The Case of Child Underutrition in East Java
Fatkhi Rizqiyah Agustina, Bambang Widjanarko Otok, Santi Wulan Purnami

Department of Statistics, Faculty of Science and Data Analytics, Institut Teknologi Sepuluh Nopember, Kampus ITS -Sukolilo, Surabaya 60111, Indonesia


Abstract

Structural equation modeling (SEM) is a statistical technique that can explain relatively complex relationship structures involving many variables. This is a structural equation model. Fulfillment of parametric distribution assumptions is often difficult to fulfill, so Partial Least Square (SEM-PLS) is a good alternative to overcome these limitations. SEM-PLS assumes that the sample taken comes from a homogeneous population. Whereas in research, many variables and indicators were involved which were collected from populations with different characteristics resulting in heterogeneity in the data. There are two kinds of data heterogeneity, namely observed heterogeneity and unobserved heterogeneity. Ignoring unobserved heterogeneity will lead to some research errors. One method to overcome this is prediction-oriented segmentation PLS (POS-PLS). One aspect with unobserved heterogeneity is the health aspect, which is related to malnutrition. Inadequate nutrition or often known as malnutrition has a very broad impact, not only having a big role in increasing morbidity and mortality but also having a role in disrupting psychosocial aspects and intellectual development. Malnutrition can affect anyone, but infants and toddlers are the most vulnerable group because they require high levels of nutrients for growth and development. Stunting, wasting, and being underweight are expressions of a lack of energy and protein intake, infectious diseases, and also the result of malnutrition during pregnancy. Nutritional status is influenced by 3 factors, namely direct, basic, and enabling factors that formed into latent variables. The endogenous latent variables used were food, practice, and service. The exogenous latent variable is social economy.

Keywords: POS-PLS, SEM-PLS, Stunting, Underweight, Wasting

Share Link | Plain Format | Corresponding Author (Fatkhi Rizqiyah Agustina)


76 Mathematics and Statistics ABS-21

Forecasting Volatility of Sukuk Price Return with Markov-Switching GARCH (Case Study: Franklin Global Sukuk Fund Luxembourg)
Chandrawati (a*), Irhamah (a), Nur Iriawan (a)

a) Department of Statistics, Institut Teknologi Sepuluh Nopember (ITS), Sukolilo, 60111, Indonesia.
*chandrawatimtk[at]gmail.com


Abstract

Volatility is a variance that changes over time. Volatility in an investment is defined as a measure of the risk associated with a portfolio based on price changes, therefore volatility is one of the most important risk indicators for Islamic financial market players and observers. One of the Islamic financial market products is sukuk. Sukuk or sharia bonds are certificates with the same value representing the full ownership of the basic assets, benefits and services of a project or special investment activity. Changes in sukuk prices have an impact on sukuk returns, hence good management is needed for sukuk investors to get the expected return. Franklin Global Sukuk Fund is a sukuk is a sukuk issued by the state of Luxembourg. The time series data on the Franklin Global Sukuk Fund undergoes a structural change in the volatility shift of the sukuk return, hence an appropriate model is needed to describe it. The research will predict the volatility of sukuk returns with the model Markov-Switching GARCH. MSGARCH can analyze structural changes and shifts in the volatility of sukuk returns and predict volatility for future periods. Thus, the best Markov-Switching GARCH model will be estimated by Bayesian method, namely Markov Chain Monte Carlo (MCMC) and Hamiltonian Monte Carlo (HMC).

Keywords: HMC, MCMC, MSGARCH, Sukuk, Volatility

Share Link | Plain Format | Corresponding Author (Chandrawati Chan)


77 Mathematics and Statistics ABS-22

Forecasting of Indonesian Crude Oil Price using EEMD- LSTM
Nuchaila Ainiyah (a*), Heri Kuswanto (a), Kartika Fithriasari (a)

(a) Department of Statistics, Institut Teknologi Sepuluh Nopember (ITS), Sukolilo, 60111, Indonesia
*nuchela24[at]gmail.com


Abstract

Crude oil is a commodity that plays a very important role in all economies. The direct impact of fluctuations in crude oil prices is changes in operational costs. The development of Indonesia^s crude oil price has recently been trending throughout early January, so this has caused the crude oil price chart to fluctuate. The instability of crude oil prices was preceded by an increase in oil prices. Ensemble empirical mode decomposition (EEMD) was employed to decompose runoff series into several stationary components and a trend. The long short-term memory (LSTM) model was used to build the prediction model for each sub-series.The model input set contained the historical flow series of the simulation station its upstream station and the historical meteorological element series. The final input of the LSTM model was selected by MI method. To verify the effect of EEMD, this study used the Radial Basis Function (RBF) model to predict the sub-series, which was decomposed by EEMD. This study aims to predict price of Indonesian crude oil using Ensemble empirical mode decomposition (EEMD) and long short-term memory (LSTM).

Keywords: Crude Oil, EEMD, LSTM

Share Link | Plain Format | Corresponding Author (Nuchaila Ainiyah)


78 Mathematics and Statistics ABS-23

Smooth Support Vector Machine Based on Polynomial Function for Depression Detection Using Electroenchephalogram (EEG) Signal
Annisatul Nikmah (a), Santi Wulan Purnami (a*), Shofi Andari (a), Margarita M. Maramis (b), Wardah R. Islamiyah (c), Jasni Muhammad Zain (d)

a) Department of Statistics, Faculty of Science and Data Analytics, Institut Teknologi Sepuluh Nopember, Surabaya 60111, Indonesia
*santi_wp[at]statistika.its.ac.id
b) Department of Psychiatry, Faculty of Medicine, Airlangga University, Surabaya 60131, Indonesia
c) Department of Neurology, Faculty of Medicine, Airlangga University, Surabaya 60131, Indonesia
d) Institute for Big Data Analytics and Artificial Intelligence(IBDAAI), Universiti Teknologi Mara (UiTM), Shah Alam 40450, Malaysia


Abstract

Mental health is an important issue today as mental illness as a global health problem ranks fifth in the world. Depression is a major illness that affects many people around the world and people suffering from depression often have a low level of awareness. It is still common to detect depression using clinical questionnaires. However, using questionnaires for large-scale surveys will consume large human and material resources. Therefore, scientists and researchers from around the world are working to find alternative and objective ways to detect mental depression, especially through EEG signal data. Several studies have shown that abnormal patterns in alpha waves in EEG signals are associated with depression, but beta, delta, theta, and gamma waves can also be used for depression detection. EEG signal preprocessing is required before classification by filtering using Finite Impulse Response (FIR). Furthermore, EEG signal data will be classified using one of the Machine Learning methods, namely Support Vector Machine (SVM) because from some existing research SVM provides superior performance compared to other methods. This research proposes Piecewise Polynomial Smooth Support Vector Machine (PPWSSVM) and Spline Smooth Support Vector Machine (Spline SSVM) for the classification method and data will be taken from patients at the Psychiatric Poli Dr. Soetomo Hospital. The results of this study are expected to be able to provide assistance and alternative methods related to the objective diagnosis of depression.

Keywords: Depression-EEG-PPWSSVM-Spline SSVM

Share Link | Plain Format | Corresponding Author (Annisatul Nikmah)


79 Mathematics and Statistics ABS-24

Semiparametric Bivariate Probit Model Using Newton Raphson Approach Early Breastfeeding Initiation and Exclusive Breastfeeding
Suci Amalia, Vita Ratnasari*, Ismaini Zain

Department of Statistics, Faculty of Science and Data Analytics, Institut Teknologi Sepuluh Nopember, Surabaya 60111, Indonesia
*vita_ratna[at]statistika.its.ac.id


Abstract

Regression analysis in which the response variable is categorical can be processed using the probit model. The probit model is based on the normal distribution, in addition to its interpretation based on marginal effect values. A probit model consisting of two response variables is called the bivariate probit model, in which the response variables each consist of two categories. The predictor variables in bivariate probit model can be either categorical and also continuous data. Bivariate probit model both response variables have a relationship. One of the developments of the bivariate probit model is the semiparametric bivariate probit model, where the bivariate probit model in which there is a parametric and a nonparametric model in this case in the form of a continuous covariate smooth function. Semiparametric bivariate probit model have the advantage of being able to address the problem of nonlinearity of undetected continuous predictor variables that can cause modeling inaccuracies that can effect the results of estimation accuracy. Parameter estimation of semiparametric bivariate probit model uses the Penalized Maximum Likelihood Estimation approach, but the equation obtained is not closed form so iteration are needed to solve it. The iteration used is Newton Raphson. The case study is data on early breastfeeding initiation and exclusive breastfeeding in East Java Province in 2021 obtained from the SUSENAS (National Sosioeconomic Survey) of Badan Pusat Statistik (BPS).

Keywords: Early Breastfeeding Initiation- Exclusive Breastfeeding- Newton Raphson- Penalized Maximum Likelihood Estimation- Semiparametric Bivariate Probit

Share Link | Plain Format | Corresponding Author (Suci Amalia)


80 Mathematics and Statistics ABS-25

Parameter Estimation of Geographically Weighted Compound Correlated Bivariate Poisson Regression Model
Rizki Safarida(a*),Purhadi(a),Sutikno(a)

a)Departement of Statistics,
Institut Teknologi Sepuluh Nopember
Kampus ITS-Sukolilo, Surabaya 60111,Indonesia
*rizkisafarida[at]gmail.com


Abstract

Compound Correlated Bivariate Poisson Regression (CCBPR) is a regression model that combines the Poisson distribution with other distributions that is proposed to overcome overdispersion issue on correlated count data which has high skewness/long tail. Geographically Weighted Compound Correlated Bivariate Poisson Regression (GWCCBPR) is a modified model of CCBPR that consider spatial effect that occur on the data. In this study, GWCCBPR is approached by Generalized Invers Gaussian (GIG) distribution. The aim of this study is to obtain parameter estimation and hypothesis testing for the model GWCCBPR by adding exposure variable. An exposure is included in the model to account for population size difference of the analysis units. The estimation procedure is conducted by using Maximum Likelihood Estimation and BHHH algorithm.

Keywords: BHHH algorithm- Exposure- Geographically Weighted Compound Correlated Bivariate Poisson Regression.

Share Link | Plain Format | Corresponding Author (Rizki Safarida)


81 Mathematics and Statistics ABS-26

Identification of Tomato Ripeness Using RGB Color Image Analysis
Firda Fadri (a*), Kiswara Agung Santoso (a)

a) Jember University
Jalan Kalimantan No.37 Kampus Bumi Tegalboto, Jember 68121 Indonesia
*firdafadri[at]unej.ac.id


Abstract

The identification of tomato fruit ripeness is performed to assess fruit quality. The identification process relies on fruit images using image processing techniques. The research data is leveled into four ripeness levels: unripe, half-ripe, ripe t, and rotten tomatoes. The RGB color space is utilized to classify the test image data. Correlation coefficient values and MSE values are obtained from feature extraction. The highest correlation coefficient for each test data indicates the fruit category, aligning with the classification results as expected. The classification of the test image data with the training image data achieves an accuracy rate of 85%. The average MSE values for each ripeness category are exceptionally small (approaching zero), indicating minimal differences between the test image data and the training image data.

Keywords: Tomato- Image Processing- RGB

Share Link | Plain Format | Corresponding Author (firda fadri)


82 Mathematics and Statistics ABS-28

Max Charts Performance in Monitoring Water pH
Niam Rosyadi, Muhammad Ahsan, Muhammad Mashuri

Institut Teknologi Sepuluh Nopember Surabaya


Abstract

Control charts are statistical tools used to monitor the stability of a process over time. Its used to detect changes in the mean or variability of a process, which can indicate the need for corrective action. The Max chart is a type of control chart that can be used to monitor both the mean and variability of a process simultaneously. It is a more powerful tool than traditional control charts, as it can detect smaller changes in the process. In this study, the Max chart was used to monitor the water pH of a shrimp pond in Madura, Indonesia. The data consisted of 116 samples, and the monitoring results using &#945-=0,0027 showed that 114 of the samples were in control, while 2 were out of control. This indicates that the water pH in the pond was stable for most of the time, but there were two instances where the pH changed significantly. The results of this study suggest that the Max chart is a valuable tool for monitoring the water quality of shrimp ponds. It can be used to detect changes in the water pH, which can help to ensure that the shrimp are living in a healthy environment

Keywords: control chart, max chart, water pH, shrimp pond, Madura, Indonesia

Share Link | Plain Format | Corresponding Author (Niam Rosyadi)


83 Mathematics and Statistics ABS-29

Partial Hypothesis Testing on Mixed Nonparametric Regression of Spline Truncated and Fourier Series (Case Study: Percentage of Poverty Regency/City in West Java 2021)
Bryllian Reyga Akbar Pramadana (a*), I Nyoman Budiantara (a), Vita Ratnasari (a)

a) Department of Statistics, Faculty of Science and Data Analytics, Institut Teknologi Sepuluh Nopember (ITS), Sukolilo, Surabaya, 60111, Indonesia
*bryllianr[at]gmail.com


Abstract

In regression analysis, the regression curve estimation can be done with several approaches including parametric, nonparametric, and semiparametric approaches. The nonparametric approach is used if the shape of the regression curve is unknown and does not follow a certain pattern. Several parameter estimation approaches of nonparametric regression models are Kernel, Fourier Series, and Spline. In reality, not all predictor variables have the same data pattern, so a mixed estimator is needed to solve the problem. The predictor variables that are thought to have an influence are open unemployment rate, literacy rate, average length of schooling, and GRDP growth rate. As the development of previous research, a mixed nonparametric regression model of spline truncated and fourier series will be estimated using Ordinary Least Square (OLS) optimization. Through the theoretical study, it will be obtained the hypothesis statement, the test statistics and its approximation distribution, and the critical region. The test statistics used in the partial hypothesis testing was obtained using the Likelihood Ratio Test (LRT). Parameter estimation and partial hypothesis testing of the mixed nonparametric regression model of spline truncated and fourier series will be applied to Percentage of Poverty data in West Java 2021.

Keywords: Nonparametric Regression- OLS- Spline Truncated- Fourier Series- LRT

Share Link | Plain Format | Corresponding Author (Bryllian Reyga Akbar Pramadana)


84 Mathematics and Statistics ABS-30

Selecting of Optimal Knot Points and Oscillation Parameters Using Generalized Cross-Validation (GCV) and Unbiased Risk (UBR) Method in Nonparametric Regression of Combined Estimators Spline Truncated dan Fourier Series
Putri Kusuma Wardani (a), I Nyoman Budiantara (a*), Setiawan (a)

a) Department of Statistics, Faculty of Science and Data Analytics, Institut Teknologi Sepuluh Nopember, Sukolilo, Surabaya 60111, Indonesia
*i_nyoman_b[at]statistika.its.ac.id


Abstract

If the shape of the pattern between the response variables and the predictor variables is not known, then the approach that is suitable for this case is a nonparametric regression approach. There are several methods in nonparametric regression such as spline truncated and Fourier series. In spline truncated nonparametric regression determining the optimal knot point is very important and crucial, as is in fourier series nonparametric regression which determines the oscillation parameters. Determination of the knot points and oscillation parameters in nonparametric regression of combined estimators spline truncated and fourier series will affect the regression curve that will be formed. There are several methods that can be used in selecting optimal knot points and oscillation parameters, namely the Generalized Cross-Validation (GCV) and Unbiassed Risk (UBR) methods. The aim of this study was to examine the GCV and UBR methods to select knot points and optimal oscillation parameters in nonparametric regression of combined estimators spline truncated and fourier series. Then a comparison of the selection of knot points and oscillation parameters using the GCV and UBR methods on the data on the rate of economic growth Indonesia in 2022. The estimation method used is Ordinary Least Square (OLS).

Keywords: Fourier Series- Generalized Cross-Validation- Nonparametric Regression- Spline Truncated- Unbiased Risk

Share Link | Plain Format | Corresponding Author (Putri Kusuma Wardani)


85 Mathematics and Statistics ABS-31

Performance Comparison of Max-Chart and EWMA-Max Chart in Monitoring Salinity
Salman Alfarizi P.A.(a*), Muhammad Ahsan (a), Muhammad Masuri (a), Kevin Agung Fernanda Rifki (a)

a) Department of Statistics, Sepuluh Nopember Institute of Technology Surabaya, Indonesia


Abstract

Statistical Process Control (SPC) is a widely used statistical technique to ensure that a process meets certain criteria. SPC itself is used to identify process shifts quickly and minimize the level of damage to the product. SPC are production methods to achieve maximum efficiency, productivity and quality to produce competitive products. This study proposes a new method for monitoring salinity data in vannamei shrimp ponds using the EWMA-Max control chart. The proposed method was compared to the traditional EWMA control chart and the Max-EWMA control chart. The results showed that the EWMA-Max control chart was more effective in detecting small and large shifts in the mean of the salinity data. The optimal parameters for the EWMA-Max control chart were &#955- = 0.1 and L = 2.57. The EWMA-Max control chart with these parameters was able to detect 28 out of control data and 47 in control data.

Keywords: Statistical Process Control, Salinity, Univariate, Max-Chart,EWMA-Max.

Share Link | Plain Format | Corresponding Author (Salman Alfarizi Pradana Andikaputra)


86 Mathematics and Statistics ABS-32

Curve Estimation of Multivariable Nonparametric Kernel Regression on the Percentage of Households with Access to Decent and Affordable Housing
Tiaranisa^i Fadhilla, I Nyoman Budiantara, and Ismaini Zain

3Institut Teknologi Sepuluh Nopember


Abstract

Nonparametric regression methods, such as spline, Fourier, and kernel regression, are essential for modeling real cases where the relationships between variables cannot be easily defined. Among these methods, kernel regression is particularly useful when the underlying data patterns are unknown and do not follow a specific trend, periodicity, or interval-based changes. This research focuses on obtaining curve estimates through kernel regression using multiple predictor variables. The study aims to enhance our understanding of multivariable kernel regression and its practical applications. The bandwidth selection method employed is Generalized Cross Validation. The research investigates the percentage of households with access to decent and affordable housing, considering predictor variables like population density, floor area per capita, access to drinking water, and access to sanitation. The study focuses on cities and districts in Java Island, encompassing six provinces: DKI Jakarta, West Java, Central Java, DI Yogyakarta, East Java, and Banten, with a total of 119 observations. The relationship patterns observed between the predictor variables indicate non-monotonic associations, where an increase in the predictor value does not necessarily correspond to an increase or decrease in the response value. Consequently, the research employs kernel nonparametric regression with multiple variables to address this complexity.

Keywords: Affordable Housing, Curve Estimation, Generalized Cross Validation, Kernel, Nonparametric Regression

Share Link | Plain Format | Corresponding Author (Tiaranisai Fadhilla)


87 Mathematics and Statistics ABS-35

FORECASTING INDONESIA GOLD PRICE USING SETAR AND SETAR-TREE
Aurell Faza Ashilla(a*), Heri Kuswanto(a), Nur Iriawan(a)

a) Department of Statistics, Institut Teknologi Sepuluh Nopember (ITS), Sukolilo, Surabaya 60111, Indonesia
*aurellashilla[at]gmail.com


Abstract

Gold is used as a financial standard in many countries and also as a relatively enduring and accepted medium of exchange across countries. Gold was chosen as an investment instrument because it is liquid or easily converted into cash as a legal medium of exchange. In addition, the advantages of investing in gold are low risk, as a hedging tool, and prices that are not affected by interest rate policies. Even though the investment risk is low, not all gold investors can make a profit from the gold price. When viewed from the price movements that tend to fluctuate and have high volatility, the price of gold can contain a non-linear component. In order to accommodate nonlinear patterns in gold prices, nonlinear modeling is needed to predict gold prices in the future. The method used in this research is SETAR and SETAR-Tree to predict the price of Indonesian gold. Based on the results of the analysis carried out, in the in sample and out sample modeling, SETAR(2,1,1) and SETAR-Tree have almost the same performance because when compared through AIC values, the SETAR-Tree model has a smaller AIC value . Meanwhile, when compared through RMSE and MAPE values, the SETAR(2,1,1) model has smaller RMSE and MAPE values. In this study, a simulation was also carried out on the generated data following SETAR(2,2,2) with a different amount of data, namely 200 and 2000 data. Based on the simulation results, the SETAR and SETAR-Tree model has the same performance both for data with a small amount of data and a large amount of data.

Keywords: Gold Price, Nonlinear, Forecasting, Trees Regression, SETAR, SETAR-Tree

Share Link | Plain Format | Corresponding Author (Aurell Faza Ashilla)


88 Mathematics and Statistics ABS-38

PARAMETERS ESTIMATION AND HYPOTHESIS TESTING OF CUBIC SEMIPARAMETRIC RECURSIVE BIVARIATE PROBIT REGRESSION MODEL
Abdullah Fahmi (a), Purhadi (b), Jerry Dwi Trijoyo Purnomo (c)

(a) Department of Statistics, Institut Teknologi Sepuluh Nopember (ITS), Sukolilo, 60111, Indonesia
(b) Department of Statistics, Institut Teknologi Sepuluh Nopember (ITS), Sukolilo, 60111, Indonesia
purhadi[at]statistika.its.ac.id
(c) Department of Statistics, Institut Teknologi Sepuluh Nopember (ITS), Sukolilo, 60111, Indonesia
jerrypurnomo[at]gmail.com


Abstract

The cubic semiparametric recursive bivariate probit regression model is a model that describes the relationship between two response variables in the form of binary categorical data with one or more predictor variables in the form of categorical data and continuous data by considering the endogeneity problem. This endogeneity problem is a model case where endogenous variables can become exogenous variables. A cubic semiparametric recursive bivariate probit regression model to overcome the problem of inconsistent and biased parameter estimates. This study aims to estimate parameters using the Penalized Likelihood Estimation and to test the hypothesis using the likelihood ratio test, which is a simultaneous and partial significance test. Because the log function for the first possible derivative is not in a close form, it uses a numerical iteration method, namely fisher scoring iterations until it convergence.

Keywords: Cubic Semiparametric Recursive Bivariate Probit, Penalized Likelihood Estimation, Fisher Scoring

Share Link | Plain Format | Corresponding Author (Abdullah Fahmi)


89 Mathematics and Statistics ABS-41

Confidence Intervals For Parameters Of The Biresponse Truncated Spline Nonparametric Regression Model
Rizka Amalia Putri*, I Nyoman Budiantara, Vita Ratnasari

Department of Statistics, Faculty of Science and Data Analytics, Institut Teknologi Sepuluh Nopember


Abstract

Confidence interval is one of the most important parts of statistical inference. Many ways have been done to obtain confidence intervals for nonparametric regression based on the estimation method used. Previous studies discussed the confidence interval for regression model parameters using the Bayesian approach, while in this study the construction of the confidence interval was carried out using the pivotal quantity method, because it was considered easier because it did not involve a prior distribution. Confidence intervals for nonparametric regression parameters can be used to determine which predictor variables significantly affect the response variable. In this study, confidence intervals will be developed for model parameters using several predictor variables and two response variables. If two response variables are found to be correlated, then the modeling can use a birresponse regression model. The purpose of birresponse regression modeling is to get a better model than single response modeling, with a regression model that not only considers the effect of predictors on the response, but also the relationship between responses. The approach in nonparametric regression used in this study is truncated spline. Truncated splines are segmented and continuous polynomial pieces that have connection points called knot points. In this study, the optimum knot point selection is seen based on the minimum Generalized Cross Validation (GCV) value. The results obtained obtained confidence intervals for nonparametric birresponse truncated spline regression parameters when the population variance is known and confidence intervals for parameters when the population variance is unknown. Based on the results obtained, it shows that the confidence intervals for the parameters of birespon nonparametric truncated spline regression are similar to the confidence intervals for classical regression, but the constituent elements are different.

Keywords: nonparametric regression-biresponse truncated spline nonparametric regression-parameter confidence interval

Share Link | Plain Format | Corresponding Author (Rizka Amalia Putri)


90 Mathematics and Statistics ABS-42

Confidence Intervals for Curve of Biresponse Truncated Spline Nonparametric Regression
Mardiyah Muhgni*, I Nyoman Budiantara, Vita Ratnasari

Department of Statistics, Faculty of Science and Data Analytics, Institut Teknologi Sepuluh Nopember, Kampus ITS-Sukolilo, Surabaya.


Abstract

One of the objectives of statistical analysis is to obtain point estimates and interval estimates for parameters or regression curves. Confidence intervals are part of inferential statistics along with point estimates. Confidence intervals have the advantage of a smaller error probability value, where the regression curve confidence interval is able to describe the upper and lower limits of the resulting regression curve. The statistical method used to determine the relationship between response variables and predictor variables whose function form is unknown is the nonparametric regression approach which is only assumed to be smooth in the sense that it is contained in a certain function space. Spline nonparametric regression is one of the most widely used methods in nonparametric regression. The ability of spline regression is that it can estimate data behavior that tends to be different at different intervals and has high flexibility. This ability to estimate data can be done with a function that has been attached to the estimator and a part called the knot point in nonparametric regression. The optimum knot point selection is done by looking at the minimum Generalized Cross Validation (GCV) value. This study will involve two response variables and several predictor variables called biresponse regression which aims to get a better model than single response modeling because the regression model not only considers the effect of predictors on the response, but also the relationship between responses. This study aims to obtain confidence intervals for birespon truncated spline nonparametric regression curves with known population variance and unknown population variance.

Keywords: Nonparametric regression - Curve confidence interval - Biresponse truncated spline nonparametric regression.

Share Link | Plain Format | Corresponding Author (Mardiyah Muhgni)


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