基于截尾数据概率密度核估计的一些渐近行为(英文)

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

Blum和Snsarla(1980)提出了一基于截尾数据非负随机变量概率密度f(t)的核估计(?)_n(t),本文证明了(?)_n(t)的一致强相合性。此外,我们还进一步研究了(?)_n(t)的一致强收敛速度问题,给出了(?)_n(t)的一渐近表达式,并利用所给的表达式证明了(?)_n(t)以速度为O(n^(-2a))均方收敛到(?)_n(t),其中0<a<1/4。

We consider the kernel estimator fn(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 fn(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 fn(t) converges in mean square to- f(t) with rate 0(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.