随机截断下基于多个混合分布样本的非参数推断

Nonparametric Inference with Stochastic Censored Data for Multi-mixture Distributions

设有K族(K≥2)i.i.d.(独立同分布)随机变量{Xij,j=1,2,…,ni},i=1,2,…,K,分别来自于分布Gi(x)=(1-iα)F1(x)+iαF2(x),其中iα∈[0,1].每族随机变量同时被另一列i.i.d.随机变量Yij,j=1,2,…,ni截断.本文分别用经验分布和Kaplan-meier估计构造了分布F1,F2的估计,并证明了估计量的性质.最后用数值例子对两种方法作了比较,验证了Kaplan-meier估计的精确有效性.

Suppose {Xy,j=1,2,…,ni},i=1,2,…,K are K（K≥2） sequences of i.i.d, random varables with the distribution functions of Gi （x）=（1-αi） F1 （x）＋αiF2 （x） respectively, where αi∈[0,1]. Under the assumption： the datas defined as above are truncated by others i. i. d. Yy,j =1,2,…, ni, this paper presents the estimation of F1, F2 by experiential and Kaplan-meier method, proves their asymptotic properties. The two methods are compared by a numerical simulation and the exactness and effiency of the Kaplan-meier estimators are validated.