讲座主题：Empirical likelihood for partially linear single-index models withmissing observations

报告人：薛留根（北京工业大学教授、博导）

时间：2022年10月17日9:00-11:00

线上会议：腾讯会议号208-210-016

报告人简介：薛留根，北京工业大学教授，河南大学特聘教授，博士生导师。主要学术兼职：中国现场统计研究会理事及生存分析分会副理事长等。研究方向：非参数统计与数据分析。主要研究兴趣包括：非参数与半参数模型的统计推断、复杂数据的统计分析与建模、经验似然等。主持国家和省部级科研项目15项，其中连续5次获国家自然科学基金资助。在《Annals of Statistics》、《JASA》、《JRSSB》、《Biometrika》等学术期刊上发表论文260余篇，其中3篇为高被引论文。出版著作8部，其中4部专著。以第一完成人获教育部自然科学二等奖1项，获全国统计科学研究优秀成果一等奖1项。已培养博士研究生20人、硕士研究生45人；在指导的研究生中，1人获北京市优秀博士学位论文以及全国优秀博士学位论文提名奖，1人获全国统计科学研究优秀博士学位论文二等奖。

报告内容：  In this talk, we study theempirical likelihood for a partially linear single-index model with a subset ofcovariates and response missing at random. By using the bias-correction and theimputation method, two empirical log-likelihood ratios are proposed such thatany of two ratios is asymptotically chi-squared. Two maximum empiricallikelihood estimates of the index coefficients and the estimator of linkfunction are constructed, their asymptotic distributions and optimalconvergence rate are obtained. It is proved that our methods yieldasymptotically equivalent estimators for the index coefficients. An importantfeature of our methods is their ability to handle missing response and/orpartially missing covariates. In addition, we study the estimation andempirical likelihood for two special cases—the single-index model and partiallylinear model with observations are missing at random. A simulation studyindicates that the proposed methods are comparable for bias and standarddeviation, as well as in terms of coverage probabilities and average areas(lengths) of confidence regions (intervals). The proposed methods areillustrated by an example of real data.