Nonparametric Estimation of the Conditional Quantiles

Abstract

Nonparametric kernel estimators are widely used in many research areas of statistics. An important nonparametric kernel estimators of the conditional quantiles are the Nadaraya-Watson and Weighted Nadaraya-Watson kernel estimation of the conditional quantiles which is often obtained by using a xed bandwidth. One of the important issues in kernel smoothing is the choice of the smoothing parameters. In this thesis, we propose a new method of smoothing for nonparametric conditional quantile which depends on di erent bandwidths. We consider the adaptive Nadaraya-Watson kernel estimation of the conditional quantiles and the adaptive Weighted Nadaraya-Watson kernel estimation of the conditional quantiles. The results of the simulation studies show that the adaptive Nadaraya-Watson kernel estimation and the adaptive Weighted Nadaraya-Watson estimation have better performance than the kernel estimations with xed bandwidths