Comparison of Kernel Functions to Estimate Nonparametric Confidence Limits with Application

Abstract

Nonparametric confidence bound estimation is a statistical technique used to estimate the probability density function, which works to smooth each point in the data of the variable to be studied. Nonparametric confidence intervals define an interval containing the core function based on the sample data, which is defined by an upper and lower bound. In this research, a comparison was made between the nonparametric kernel functions in the case of estimation with nonparametric confidence intervals using the plug-in approach method. It was noted that all the functions gave good results through the graph in the case of using real data, and the best functions were the Epanechnikov and the Tricube functions for estimating the kernel function with nonparametric confidence intervals, where the confidence intervals were narrow in the graph.