一、题目

A beyond multiple robust approach for missing response problem

二、主讲人

王启华

三、摘要

Imputation and the inverse probability weighting are two commonly used approaches in missing data analysis. Parametric versions of them are not robust due to model misspecification of some unknown functions. Nonparametric ones are robust but are impractical when the number of covariates is large due to the problem of “curse of dimension”. A beyond multiple robust method is proposed in this paper. This method balances the parametric and nonparametric methods by using some model information contained in the outcome regression function and the selection probability function, and hence alleviates the model misspecification problem and “curse of dimension” problem simultaneously. To illustrate the proposed method, we focus on the estimating problem of response mean in the presence of missing responses. A beyond multiple robust estimator of the response mean is defined, which is proved to be consistent and asymptotically normal as long as one of the true models for the outcome regression or selection probability functions can be some function of its assumed models, without the requirement that one of the true models is correctly specified. Also, it is shown that the asymptotic variance of the proposed estimator is equal to the semiparametric efficiency bound established by Hahn (1998, Econometrica, pp 315-331) when both the selection probability function and the outcome regression function are the functions of their assumed models, respectively. The finite sample properties of the proposed estimator are evaluated by simulation studies and the proposed method is illustrated by a real data analysis.

四、主讲人简介

王启华，中国科学院数学与系统科学研究院研究员，博士生导师，国家杰出青年基金获得者，教育部长江学者奖励计划特聘教授，中科院“百人计划”入选者，首届全国百篇优秀博士论文奖获得者。曾在北京大学与香港大学任教，先后访问加拿大Carleton大学、美国California大学戴维斯分校、美国California大学洛杉矶分校、美国Yale大学、美国华盛顿大学、美国西北大学、德国Humboldt大学、澳大利亚国立大学及澳大利亚悉尼大学等。主要从事生存分析、缺失数据分析、高维数据统计分析及非-半参数统计推断等方面的研究。出版专著三部，在The Annals of Statistics, JASA及Biometrika等国际重要刊物发表论文百余篇。是高维统计分会理事长，分别是生存分析及生物统计分会副理事长，先后是IMS-China和IBS-China委员会委员，是一些国际与国内学术期刊的编委。

五、时间

3月30日（周二）11:00-12:00

六、地点

中心校区知新楼B座1248报告厅

七、主办方

山东大学数学学院