Nonlinear wavelet shrinkage estimator of nonparametric regularity regression function via cross-validation with simulation study

摘要

Nonparametric regression techniques provide a very effective and simple way of finding structure in data sets without the imposition of a parametric regression model. Wavelet theory has the potential to provide statisticians with powerful new techniques for nonparametric inference. In this paper, we consider the wavelet shrinkage kernel estimator of regression function with a common one-dimensional probability density function. We investigate a new nonparametric curve estimator and convergence ratio of given estimator by using cross-validation method to choice of wavelet threshold when the observations are taken on the regular grid. At the end we used simulation study to examine our proposed estimator. We survey the theoretical outcomes with numerical computation by using R software to compare purpose estimator with another estimators.