协变量带误差的随机删失数据线性模型的一类半参数估计

A Class of Semiparametric Estimators for Linear Error-in-Covariables Models Under Random Censorship

考虑线性模型Yi=Xi^Tβ＋εi,i=1，2，…，n，其中Yi为随机右删失因变量，Xi难以观测，或需要较高成本才能得到其精确观测值，故转而观测与Xi相关的相对易得的随机变量Xi利用数据集{（Xj，Xj）}n＋N,j=n＋1估计E[X｜X^-]的同时，给出了参数向量β的一类半参数估计，并且证明了估计量的渐近正态性．

Consider the linear models Yi=Xi^Tβ＋εi,i=1,2,…,n, with the response Yi censored randomly on the right and Xi hard or costly to measure. A relative variable X^- is to be measured instead of X. When estimating E[ X｜X] with the help of validation data{（Xj,Xj）}n＋N,j=n＋1, a class of semiparametric estimators for vector β are given and the asymptotic normality is also proved.