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

Topic: Mathematics and Statistics