SOME ASYMPOTOTIC BEHAVIOURS OF THE KERNEL ESTIMATOR OF A DENSITY FUNCTION BASED ON CENSORED DATA

We consider the kernel estimator \hatf_n(t) of density f（t） of nonnegative random variates based on censored date proposed by Blum and Susarla （1980）. In this paper, uniformly rtrong consistency of the estimator\hatf_n(t). is investigated. The convergence rate of uniformly strong consistency and a asympototic representation of the estimator proposed are also given, respectively. Moreover the asympototic representation is used to show that \hatf_n(t) converges in mean square to f（t） with rate O（n^-2α）, where 0＜α＜1/4. Key words and phrase.Kernel Estimator; Censored Data; Uniformyl strong consistency; Convergence Bate; Arympototic Representation; Convergence In Mean Square.