Based on empirical likelihood method, we investigate statistical inference in partially linear single-index quantile regression with high dimensional linear and single-index parameters when the observations are missing at random, which allows the response or covariates or response and covariates simultaneously missing. In particular, applying B-spline approximation to the unknown link function, we establish asymptotic normality of bias-corrected empirical likelihood ratio function and maximum empirical likelihood estimator of the parameters; variable selection are considered by using the SCAD penalty. Meanwhile, we propose a penalized empirical likelihood ratio statistic to test hypothesis, and prove its asymptotically chi-square distribution under the null hypothesis. Also, simulation study and a real data analysis are conducted to evaluate the performance of the proposed methods.

报告人简介：

同济大学数学科学学院教授，博士生导师。1997年博士毕业于37000cm威尼斯，1997-1999年在中国科技大学作博士后研究。主持过国家自然科学基金面上项目5项、国际合作项目1项和教育部项目2项，发表学术论文140余篇，曾获第十一届全国统计科研优秀成果奖二等奖、重庆市自然科学二等奖以及安徽省自然科学三等奖。研究兴趣：不完全数据的统计分析，分位数回归，高维数据分析，贝叶斯分析，经验似然，变点分析。现为中国现场统计研究会高维数据统计分会常务理事，中国现场统计研究会大数据统计分会常务理事。