Bias-corrected Kullback-Leibler distance criterion based model selection with covariables missing at random

报告题目： Bias-corrected Kullback-Leibler distance criterionbased model selection with covariables missing at random

报告人： 王启华研究员(中国科学院数学与系统科学研究院)

时间地点：2019年3月22日(星期五)下午3:00-

             紫金港校区管理学院行政楼14楼1417报告厅

摘要：Let $Y$ be the responsevariable, and $(X,Z)$ the covariable vector. We consider the model selectionproblem for $f_{Y|X,Z}(y|x,z)$ with $X$ missing at random, where$f_{Y|X,Z}(y|x,z)$ is the conditional probability function of $Y$ given$(X,Z)$. Two novel model selection criteria are suggested. One is calledbias-corrected Kullback-Leibler distance (BCKL) criterion and another one iscalled empirical-likelihood-based bias-corrected Kullback-Leibler distance(ELBCKL) criterion. Both the criteria specify a parametric model, which do not need to be correct,  for $f_{X|Y,Z}(x|y,z)$,  the conditional probability function of themissing covariates given the observed variables.  It is shown, however,  that the model selection by both the proposedcriteria is consistent and that the population parameter estimators,corresponding to the selected model, are also consistent and asymptoticallynormal even if the parametric model for $f_{X|Y,Z}(x|y,z)$ is misspecified.This is a remarkable superiority of our proposed criteria to some existingmodel selection strategies. Extensive simulation studies are conducted toinvestigate the finite-sample performances of the proposed two criteria and athorough comparison is made with some related model selection methods. Thesimulation results show that our proposals perform competitively especiallywhen the conditional distribution of the missing covariates given the observedvariables is misspecified. Supplementary materials for this article areavailable online.

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报告人简介：

王启华，中国科学院核心骨干特聘研究员，博士生导师，国家杰出青年基金获得者，首届全国优秀博士论文作者，国际统计研究会当选会员（elected member）, 先后访问加拿大Carleton大学、California大学戴维斯分校、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。）出版专著两部，发表论文百余篇，其中90多篇发表在 The Annals ofStatistics,  JASA及Biometrika等国际重要刊物，是一些国际与国内刊物的主编与编委。

联系人: 张立新教授 stazlx@zju.edu.cn(浙江大学数据科学研究中心、浙江大学数学科学学院统计学研究所)