Some perspectives on the problem of model selection

Abstract

Model selection in general and variable selection in particular are fundamental problems in statistics. This thesis makes some contributions to the literature by introducing two general procedures for model selection. The first procedure can be considered as a guiding principle for designing model selection criteria that help avoid overfitting, while the second aims at selecting good models in terms of predictive performance. The thesis also introduces two novel algorithms for variable selection in very general frameworks including generalized linear models, heteroscedastic linear regression and regression with mixtures of heteroscedastic experts.