Minimising Average Risk in Regression Models

Most model selection mechanisms work in an ‘overall ’ modus, providing models without specific concern for how the selected model is going to be used afterwards. The focussed information criterion (FIC), on the other hand, is geared towards optimum model selection when inference is required for a given estimand. In this paper the FIC method is extended to weighted versions. This allows one to rank and select candidate models for the purpose of handling a range of similar tasks well, as opposed to being forced to focus on each task separately. Applications include selecting regression models that perform well for specified regions of covariate values. We derive these wFIC criteria, give asymptotic results, and apply the methods to real data. Formulae for easy implementation are provided for the class of generalised linear models. Key-words: focussed information criterion, model selection, regression models.