Bias-corrected Kullback-Leibler distance criterion based model selection with covariables missing at random
时间：2019-03-15
阅读量：432次
- 演讲人： 王启华研究员
- 时间：2019年03月22日 周五下午3：00
- 地点：紫金港校区管理学院行政楼14楼1417报告厅
- 主办单位：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
摘要：Let $Y$ be the response variable, and $(X,Z)$ the covariable vector. We consider the model selection problem 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 called bias-corrected Kullback-Leibler distance (BCKL) criterion and another one is called 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 the missing covariates given the observed variables. It is shown, however, that the model selection by both the proposed criteria is consistent and that the population parameter estimators, corresponding to the selected model, are also consistent and asymptotically normal 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 existing model selection strategies. Extensive simulation studies are conducted to investigate the finite-sample performances of the proposed two criteria and a thorough comparison is made with some related model selection methods. The simulation results show that our proposals perform competitively especially when the conditional distribution of the missing covariates given the observed variables is misspecified. Supplementary materials for this article are available online.
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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
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，中科院“百人计划”入选者，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 of Statistics, 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。