截断数据模型中的两阶段抽样序贯密度估计

TWO-STAGE SAMPLING SEQUENTIAL DENSITY ESTIMATION FROM CENSORED DATA

摘要: 令X₁,X₂,…是iid随机变量序列,满足分布F密度函数,X_i被随机变量Y_i右截断,而Y_i是iid随机变量,且与X_i独立。我们仅能观察到样本 Z_i=min（X_i,Y_i）,δ_i=I（X_i≤Y_i）估计量f_n和\hatf_n是基于KM估计量的f的核型估计,在本文中,我们基于f_n和\hatf_n分别构造f的两阶段抽样的序贯固定长度2d,渐近置信系数1-α。（0<α<1）的置信区间。并讨论了停时的渐近性质。

Abstract: Letx₁,x₂,, …be a sequence of i. i. d. random oariables with distribution function F and density function f. The X_i are censored on the right by Y_i, where the Y_i are iid. random variables and independent of X_i. We only observe the sample Z_i=min（X_i,Y_i）,δ_i=I（X_i≤Y_i） The estimator f_n（\hatf_n） based on the Kaplan-Meier estimator is the kernel-type estimate of f from Z₁, …, Z_n. In this paper, we construct a fixed-width sequantial confidence interval based on f_n（\hatf_n） Some asymptotic properties are discussed, and we give an asymptotically efficient two-stage procedure.