截断情形下污染分布的非参数估计

Nonparametric Inference with Censored Data of Contaminated Distribution

设X1,X2,…,Xn是一列iid随机变量,其分布为Fα(t)=(1-α)F1(t)+αF2(t),其中:α∈[0,1],F1(t),F2(t)都是定义在R1上的分布函数.在下列条件下:(1)上述污染数据又被另一iid的随机变量序列u1,u2,…u3截断;(2)F2(x)分布已知;(3)存在某个可测函数M(x),使μ1=∫M(x)dF1(x)已知,构造出了α和F1(x)的估计,并证明了其强相合性.

X1,X2,...Xn is a seqence of iid random varables with the distribution function of Fα(t)=(1-α)F1(t)+αF2(t) where α∈,and F1(t) and F2(t) are distribution funcions.Under the assumption:(1)the contaminaed data defined as above is truncated by another iid random variables of u1,u2,...,un,(2)The distribution function F2(x) is certain, (3)There is some measurable function such that μ1=∫M(x) d F1(x) is certain, this paper presents an estimation of α and F1(x) and proof of their strong consistency.