右删失数据下分位数回归的光滑经验似然检验  

Smoothed Empirical Likelihood Testing for Quantile Regression Models under Right Censorship

作　　者：李忠桂 何书元[1] LI Zhonggui;HE Shuyuan(School of Mathematical Sciences, Capital Normal University, Beijing, 100048, China)

机构地区：[1]首都师范大学数学科学学院,北京100048

出　　处：《应用概率统计》2019年第2期153-164,共12页Chinese Journal of Applied Probability and Statistics

基　　金：国家自然科学基金项目(批准号:11671274;11231010)资助

摘　　要：关于线性分位数回归模型的参数检验问题,对完全观测数据,已有文献用经验似然(EL)法和光滑经验似然(SEL)法构造的检验统计量在原假设下均以卡方分布χ_M^2为渐近分布.对右删失数据,已有文献用EL法构造的检验统计量以加权卡方分布为渐近分布,而权重是待估的.对右删失数据,本文用EL法和SEL法构造的检验统计量在原假设下均依分布收敛到χ_M^2,因此无需估计权重.由于SEL法的估计函数是光滑的,故可以进行Bartlett纠偏.随机模拟结果表明与已有的方法相比,SEL法经过Bartlett纠偏后有更高的精度.This paper is focused on testing the parameters of the quantile regression models. For complete observation, it is shown in literature that the test statistics, based on empirical likelihood(EL)method and smoothed empirical likelihood(SEL) method, both converge weakly to the standard Chisquare distribution χ_M^2 under the null hypothesis. For right censored data, the statistics in literature, by the EL method, have a weighted Chi-square limiting distribution, but the weights are unknown. In this paper, we show that the statistics based on the EL method and the SEL method also converge weakly to χ_M^2 under the null hypothesis, so there is no need to estimate any weights. As its estimating function is smoothed, the SEL method can be Bartlett corrected. Numerical results show that the SEL method, via Bartlett correction, outperforms some recent methods.

关 键 词：分位数回归 右删失 光滑经验似然 

分 类 号：O212.1[理学—概率论与数理统计]