A Berry-Esseen Type Bound in Kernel Density Estimation for Negatively Associated Censored Data

Abstract

We discuss the kernel estimation of a density function based on censored data when the survival and the censoring times form the stationary negatively associated (NA) sequences. Under certain regularity conditions, the Berry-Esseen type bounds are derived for the kernel density estimator and the Kaplan-Meier kernel density estimator at a fixed point $x$.