﻿ 王启华教授学术报告：Bias-corrected Kullback-Leibler distance criterion based model selection with covariables missing at random-中泰证券金融研究院 ## 博士生论坛

### 王启华教授学术报告：Bias-corrected Kullback-Leibler distance criterion based model selection with covariables missing at random

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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