Berry-Esseen bound for smooth estimator of distribution function under length-biased data.

In this paper, by using a sampling procedure, subjected to length-bias, the distribution function F is estimated by the kernel-type estimator F n s , 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. [ABSTRACT FROM AUTHOR]