Problems in Model Selection, Mixtures and Weighted Likelihood

Columbia University, New York NY

Investigators

Abstract

Abstract Problems in model selection, mixtures and weighted likelihood We study problems in model selection, mixtures and weighted likelihood. In particular, we first discuss extensions of the weighted likelihood methodology introduced by Markatou et al (1997,1998) in the context of regression models and its connection to model selection issues with emphasis in the mixture model context. We then generalize these ideas to study general model selection problems. The role of the disparity measures that are associated with weighted likelihood, and several others, is studied in detail in connection with goodness of fit approach to model selection. The point of view we take here is that parametric models can provide informative, parsimonious descriptions of the data. Then, the test statistics for testing the model adequacy are constructed and the asymptotic distributions under the null hypothesis and under contiguous alternatives are studied. The theory here is based on empirical processes. To practically implement the methods we propose to bootstrap the test statistics to obtain appropriate p-values. We consider bootstrapping from a hybrid between the model distribution stipulated by the null hypothesis and the data and study the consistency of it. When the model is false we prefer nonparametric bootstrap. The performance of Bickel's m out of n bootstrap will be examined.