核实数据下删失线性EV模型的经验似然推断

Empirical Likelihood Inference in Censored Linear Errors-in-Variables Models with Validation Data

本文考虑协变量带有误差的删失线性回归模型,借助于核实数据,对回归系数构造了两种经验对数似然比统计量,证明了所提出的估计的经验对数似然比统计量渐近收敛到一个自由度为1的独立χ2变量的加权和;而经调整后所得的调整的经验对数似然比统计量具有渐近标准χ2p分布,所得结果可以用来构造未知参数的置信域,通过模拟研究在置信域的精度及其平均区间长度大小方面进行了比较。

This paper considers censored linear errors -in -covariables regression models. We construct two empirical log - likelihood ratio statistics for the unknown regression coefficients with the help of validation data. The estimated empirical log - likelihood is proved to be asymp - totically distributed as weighted sums of independent chi - square r. v. ＇ s with I degree of freedom and the adjusted empirical log - likelihood is shown to be asymptotically distributed as standard chi - square, and hence they can be used to construct the confidence region of the parameter. A simulation study is conducted to compare the proposed methods in terms of coverage accuracies and average lengths of the confidence intervals.