Document Type: Original Paper

Author

Department of Statistics, Faculty of Mathematical Sciences, Ferdowsi University of Mashhad, Mashhad, Islamic Republic of Iran

Abstract

Kernel density estimators are the basic tools for density estimation in non-parametric statistics.  The k-nearest neighbor kernel estimators represent a special form of kernel density estimators, in  which  the  bandwidth  is varied depending on the location of the sample points. In this paper‎, we  initially introduce the k-nearest neighbor kernel density estimator in the random left-truncation model,  ‎ and then  prove some of its asymptotic behaviors, such as strong uniform consistency and asymptotic normality.  ‎In particular‎, ‎we show that the proposed estimator has truncation-free variance‎. ‎Simulations are presented to illustrate the results and show how the estimator behaves for finite samples‎. Moreover, the proposed estimator is used to estimate  the density function of a real data set.

Keywords