講座主題👱🏽‍♀️：Empirical likelihood for partially linear single-index models withmissing observations

報告人💆🏻‍♂️：薛留根（北京工業大學教授🏑、博導）

時間：2022年10月17日9:00-11:00

線上會議🫃🏻：騰訊會議號208-210-016

報告人簡介🙆🏽‍♀️：薛留根🔉😵‍💫，北京工業大學教授，河南大學特聘教授♎️，博士生導師。主要學術兼職：中國現場統計研究會理事及生存分析分會副理事長等🧓。研究方向🪆：非參數統計與數據分析。主要研究興趣包括：非參數與半參數模型的統計推斷✡︎、復雜數據的統計分析與建模🧑‍🚀、經驗似然等。主持國家和省部級科研項目15項，其中連續5次獲國家自然科學基金資助。在《Annals of Statistics》🧓🏼、《JASA》、《JRSSB》🦁、《Biometrika》等學術期刊上發表論文260余篇🚞，其中3篇為高被引論文。出版著作8部，其中4部專著🤍。以第一完成人獲教育部自然科學二等獎1項🙌🏿，獲全國統計科學研究優秀成果一等獎1項。已培養博士研究生20人、碩士研究生45人；在指導的研究生中，1人獲北京市優秀博士學位論文以及全國優秀博士學位論文提名獎，1人獲全國統計科學研究優秀博士學位論文二等獎🚵🏻‍♂️。

報告內容👥🧒🏻：  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.