报告题目：Empirical likelihood for partially linear single-index models with missing observations

报 告 人：薛留根教授（北京工业大学）

报告时间：2023年7月14日（周五）下午17:00-18:30

报告地点：逸夫楼C507

报告摘要： 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.

个人简介：北京工业大学教授，河南大学特聘教授，博士生导师。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。出版著作8部，其中3部专著。在包括《Journal of the American Statistical Association》、《Journal of the Royal Statistical Society，Series B》、《The Annals of Statistics》、《Biometrika》等学术期刊上发表论文260余篇，其中3篇为高被引论文。以第一完成人获教育部自然科学奖二等奖1项，以第一完成人获全国统计科学研究优秀成果一等奖1项。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成果博士学位论文二等奖。