應77779193永利邀請，北京工業大學數理學院薛留根教授将為我院師生作學術報告。
報告題目：Empirical likelihood for partially linear single-index models with missing observations
報告摘要：In this talk, we study the empirical likelihood for a partially linear single-index model with a subset of covariates and response missing at random. By using the bias-correction and the imputation method, two empirical log-likelihood ratios are proposed such that any of two ratios is asymptotically chi-squared. Two maximum empirical likelihood estimates of the index coefficients and the estimator of link function are constructed, their asymptotic distributions and optimal convergence rate are obtained. It is proved that our methods yield asymptotically equivalent estimators for the index coefficients. An important feature of our methods is their ability to handle missing response and/or partially missing covariates. In addition, we study the estimation and empirical likelihood for two special cases---the single-index model and partially linear model with observations are missing at random. A simulation study indicates that the proposed methods are comparable for bias and standard deviation, as well as in terms of coverage probabilities and average areas (lengths) of confidence regions (intervals). The proposed methods are illustrated by an example of real data.
報告時間：2021年7月4日下午16:00
報告地點：教學9号樓C區311會議室
邀 請 人：田玉柱副教授
屆時歡迎廣大師生參與交流！
【報告人簡介】
薛留根，北京工業大學教授，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、複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200餘篇，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。
