Using Some of Nonparametric Kernel Estimators to Estimate the Nonparametric Regression Functions with Gaussian Weight Function

Abstract

Parametric methods no longer meet the researcher\'s need due to the restrictions imposed on them because they lost flexibility in parameter estimation and data analysis. Therefore, non-parametric methods were used that because of their efficient in analyzing data without request from the researcher to make Pre-assumptions. The data and the information have the main rule to determining the function form of the studied population, and there are no parameters that represent the observations. Consequently, the purpose of estimating the nonparametric regression function is to approximate the regression function to the true regression function. Our research aims to Study and apply some nonparametric Kernel estimators for the Gaussian weight function, which are both (the localized constant regression estimator, the local linear regression estimator, and the Priestley Chow estimator. The experimental side relied on experiments Simulation on consistent data that simulates the real data that was used in the application side in representing community data, representing random errors, conducting statistical analysis and extracting results and illustrations for comparison between estimators and showing the best among them, using three criteria of comparison, average mean square error, average absolute mean error, and mean integrated square error, five different functions were assumed to generate data in the experimental side, four sample sizes, and three standard deviation values.
The important results of the experimental side are the Priestly Chow estimator show outperform of the other estimators for each of the four sample sizes and three levels of standard deviation, as well as for the five models adopted in the simulation that included the results of Kernel\'s estimators Nonparametric