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.
