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

Topic: Mathematics and Statistics