Estimation of adaptive parameters in a nonparametric regression

Abstract

The researcher faces several problems when estimating the nonparametric regression functions as they depend heavily on the data and these estimates may be inaccurate, or there may be a problem in finding an efficient method that fits the nonparametric model, so the goal is to find the adaptive capabilities in the nonparametric regression by the “Goldenshluger-lepski” method Modern methods to increase the efficiency and accuracy of estimation through the use of adaptive estimators in non-parametric regression method . In this paper, adaptive estimations were processed in the nonparametric regression method through the use of kernel smoothing and spline. The adaptive "Goldenshluger-Lepski" was included, and to compare the estimation methods three criteria were used, namely (MSE , MAS, RMSE) to choose the best method after applying the procedure to the simulation in the R Package