Berry-Esseen bound for smooth estimator of distribution function under length-biased data
Raheleh Zamini, Masoud Ajami, Vahid Fakoor · Communication in Statistics- Theory and Methods · 2022
In this paper, by using a sampling procedure, subjected to length-bias, the distribution function F is estimated by the kernel-type estimator Fns, and also a Berry-Esseen type bound for the smoothed estimator is established in this setting. Further, it is shown that the rate of the normal approximation is O(n−1/6) under some appropriate conditions.