Difficulties with the use of penalized likelihood criteria in antedependence and polynomial models
Penalized likelihoods are commonly used as model selection criteria. They involve maximizing a penalized likelihood IC(k), over a set of competing models (indexed by k). The study of their performance has been limited to asymptotic results. In normal regression models it is often possible to study finite sample properties of these criteria by formulating the likelihood in terms of residual sums of squares. Some models, like polynomial regression and antedependence models, show a natural sequence of nested alternatives. We discuss the small sample behavior of IC(k) and E(IC(k)) as functions of k for these models and present some problems that can occur with small sample sizes.