Comparison of Least Square and Penalized Least Square Methods for Estimating of Parameters in Nonparametric Regression with Fourier Series Approach Mustain Ramli (a), I Nyoman Budiantara (a*), Vita Ratnasari (a)
a) Department of Statistics, Faculty of Science and Data Analytics, Institut Teknologi Sepuluh Nopember, Kampus ITS-Sukolilo, Surabaya 60111, Indonesia
*i_nyoman_b[at]statistika.its.ac.id
Abstract
Least Square (LS) and Penalized Least Square (PLS) are the methods generally used in estimating parameters in the regression models. One of the regression models that often uses these two methods to obtain parameter estimates is the nonparametric regression model. Nonparametric regression is a regression analysis approach which assumes the regression curve is unknown and contained in a certain function space. Therefore, the nonparametric regression model can be approached with several estimator approaches, one of them is the Fourier series estimator. The Fourier series estimator is a trigonometric polynomial that has flexibility, hence can adapt effectively to the local nature of the data. Previous studies using the LS and PLS methods were limited by using one of those methods to obtain the parameter estimates in nonparametric regression model with Fourier series approach. Therefore, this study aims to use and compare the LS and PLS methods to obtain the parameter estimates in nonparametric regression with Fourier series approach and will be applied to inflation data in several cities in Indonesia during 2020. Based on the results of the analysis, the parameter estimation in nonparametric regression with Fourier series approach using the LS method only depends on the number of H oscillation parameter while the PLS method depends on the number of H oscillation parameter and Lambda smoothing parameter. To obtain the optimum number of H in the LS method can be seen by the smallest GCV(H) value in equation (11) while the optimum number of H and Lambda values in the PLS method can be seen by the smallest GCV(H,Lambda) value in equation (22).
