纵向数据缺失且具有辅助信息的光滑经验似然估计  

Smooth empirical likelihood estimation with missing longitudinal data and auxiliary information

作　　者：张雨婷 罗双华[1] ZHANG Yu-ting;LUO Shuang-hua(School of Science, Xi'an Polytechnic University, Xi'an 710048, Shaanxi, China)

机构地区：[1]西安工程大学理学院,陕西西安710048

出　　处：《宝鸡文理学院学报（自然科学版）》2021年第4期9-14,共6页Journal of Baoji University of Arts and Sciences(Natural Science Edition)

基　　金：陕西省自然科学基金项目(2020JM-571);国家自然科学基金项目(11601409);陕西省自然科学基础研究计划青年项目(2017JQ1029)。

摘　　要：目的研究纵向数据缺失且具有辅助信息的分位数回归模型的光滑经验似然估计问题。方法应用MAR随机缺失机制和辅助信息,结合分位数回归模型研究参数的光滑经验似然估计。结果在一定条件下,构造了完全数据和加权分位数光滑经验似然估计。结论在不估计复杂渐近协方差矩阵的情况下,证明了所构造的分位数光滑经验似然比服从卡方分布,并在合适的条件下证明了其渐近性质。Purposes—To study the smooth empirical likelihood estimation problem of quantile regression models with missing longitudinal data and auxiliary information.Methods—The smooth empirical likelihood estimation of parameters is studied by using MAR(missing at random)mechanism and auxiliary information and in combination with quantile regression model.Result—Under certain conditions are constructed complete data and weighted quantile smooth empirical likelihood estimators.Conclusion—Without estimating the complex asymptotic covariance matrix,it is proved that the smoothing empirical likelihood ratio of the constructed quantile obeys the chi-square distribution,and its asymptotic properties are proved under suitable conditions.

关 键 词：纵向数据缺失 分位数回归模型 辅助信息 光滑经验似然 

分 类 号：O212[理学—概率论与数理统计]