Some Problems Related to Model Selection

Texas A&M Research Foundation, College Station TX

Investigators

Abstract

Abstract PI: Gerda Claeskens Proposal ID: DMS-0203884 Title: Some problems related to model selection The first major contribution of this project is a study of nonparametric tests of function fit in the context of both density estimation and regression, hereby generalizing existing results in several directions. The proposed apparatus can be applied to test the adequacy of any parametric family, subject to the usual conditions of regularity, and is also suitable for use in higher dimensions. The second research topic focuses specifically on estimation after model selection and introduces a general approach to frequentist model averaging. A third line of research addresses the problem of generalizing the methods mentioned above to the setting of missing data. This will require the development of new model selection criteria. The goal of nonparametric testing is to construct an omnibus test, consistent against essentially any alternative model. Proposed tests are applicable to almost any parametric family of functions. There are several reasons why model selection criteria and their asymptotic properties merit further study, one of the most important ones being that only a minority of the past research provides a full integration of model selection into statistical inference. The traditional use of model selection methods in practice is to proceed as if the final selected model had been chosen a priori, without acknowledging the additional uncertainty introduced by model selection. A general framework is developed, in which several modeling and estimation strategies can be included and compared. Aspects of these problems are addressed first in the setting of complete data, and then in the general situation of missing data.