Focused Information criteria for selecting among parametric and nonparametric models


In this thesis we develop Focus Information Criteria (FIC) for a number of situations concerning model selection among nonparametric and parametric models. We mainly handle the one-sample case of fully observed independent identically distributed (i.i.d.) data, but also work in the more general setting with censored data. In addition, the regression setting and two-sample situation are discussed. Our criteria are based on asymptotic theory. Maximum likelihood theory outside model conditions and nonparametrics via statistical functionals are central. For our main criterion we state weak sufficient conditions, show strong consistency of the intermediate estimators and study the criterion’s properties both in the limit and for finite samples. It turns out that the criterion has certain desirable properties making it asymptotically superior to other information criteria like AIC and BIC in a fairly wide class of situations. We also develop weighted versions of some of the schemes and discuss the link between such a criterion and a certain class of goodness of fit tests. Model averaging is also discussed in terms of the derived schemes. We propose a model averaging generalization of the FIC schemes and derive the limiting distribution of the final estimator under a few conditions. Some of the criteria are applied to real data examples using the R function that is developed.