A Berry-Esseen Type Bound in Kernel Density Estimation for a Random Left-Truncation Model

In this paper we derive a Berry-Esseen type bound for the kernel density estimator of a random left truncated model, in which each datum (Y) is randomly left truncated and is sampled if YT, where T is the truncation random variable with an unknown distribution. This unknown distribution is estimated with the Lynden-Bell estimator. In particular the normal approximation rate, by choice of the bandwidth, is shown to be close to n^-1/6 modulo logarithmic term. We have also investigated this normal approximation rate via a simulation study.