随机右删失数据下半参数线性变换模型的经验似然推断

Empirical Likelihood Inference of Semiparametric Linear Transformation Models With Randomly Right Censored Response

本文研究了响应变量随机右删失情形下半参数线性变换模型的经验似然推断问题.构造了参数的经验似然比检验统计量,证明了经验似然比检验统计量的渐近分布为加权卡方分布.在此基础上,对经验似然比检验统计量进行了调整,证明了调整的经验似然比检验统计量的渐近分布为标准的卡方分布.基于经验似然和调整的经验似然方法,分别给出了回归参数的一定置信水平的置信域.最后对本文的方法和传统的正态逼近方法进行了模拟比较,模拟结果显示,从置信域的大小和经验覆盖概率两个角度看,本文的方法均比正态逼近方法优越.

This article develops the empirical inference method for semiparametric linear transformation models with randomly right censored response.An empirical likelihood ratio statistic is constructed and is shown to have a limiting weighted χ~2 distribution.An adjusted empirical likelihood ratio statistic is proposed based on the former one and is shown to have a limiting standard central χ~2 distribution.Confidence regions of regression parameters are then constructed.A simulation study is carried out to investigate the performance of the empirical likelihood method and the adjusted empirical likelihood method proposed in this article compared with the traditional normal approximation method.It results out that the two empirical likelihood methods have more accurate confidence regions and better coverage probabilities than the normal approximation method.