Model Selection And Model Averaging With Missing Data

Model selection is an integral part of almost any data analysis.Its main focus is on the problem of how to select an appropriate model from a sequence of plausible candi-date models for subsequent statistical inference.Model selection has been widely used in many fields such as economics,biology,and medicine.Besides,it also has been theoretically studied by many researchers for a long time.However,most of these ap-plications and researches pay attention to the case where data are observed completely while only a few of them focus on the case of missing data.Missing data occur com-monly in the study of many practical problems such as questionnaires,medical studies and socio-economic research.Thus,it is of great practical importance to develop model selection strategies that are applicable to missing data.Model averaging is a hot spot in statistics and econometrics.Unlike model selec-tion,model averaging aims at reducing the risk of estimators or forecasts by combining them across different candidate models with appropriate weights.Similar to model se-lection,most of the attention on model averaging considers the case where data are observed completely while only a few concerns with missing data.Research on the problem of model averaging with missing data is a relatively new topic for which a lot of meaningful issues remain unsolved and need further development.This dissertation studies some statistic problems related to model selection as well as model averaging in the presence of missing data.Concretely,this dissertation con-tains the following results.(1)The model selection problem for the conditional probability density function of the response given the covariates with covariates missing at random is considered.And an empirical-likelihood-based model selection criterion is proposed for the considered model selection problem.Under certain conditions,the model selection by the proposed criterion is shown to be consistent.A simulation study is conducted to investigate the finite-sample performance of the proposed criterion and a thorough comparison is made with some related model selection methods.The simulation results favor our proposal.Moreover,three real data analyses are presented for illustrating the practical application of our proposed model selection criterion.(2)We consider model averaging for linear regression models with responses miss-ing at random and data being independent and identically distributed.And we develop a model average estimation approach based on the idea of the Mallows model averaging method.The asymptotically optimality of our proposal is shown under certain condi-tions and the finite-sample performance of our proposal is investigated by simulation studies.(3)At last,we consider model averaging for linear regression models with re-sponses missing at random and non-diagonal error covariance structure.And we estab-lish a weight choice criterion based on cross validation.Under certain conditions,we show that our proposal is asymptotically optimal.And we demonstrate the superiority of our proposal over some related existing methods through simulation studies.Besides,a real data analysis is given for illustrating the practical application of our proposed model average estimation approach.