Law of iterated logarithm and strong consistency in Poisson regression model selection

Abstract

In this paper we first derive a law of iterated logarithm for the maximum likelihood estimator of the parameters in a Poisson regression model. We then use this result to establish the strong consistency of a class of model selection criteria in Poisson regression model selection. We show that under some general conditions, a model selection criterion, which consists of a minus maximum loglikelihood and a penalty term, will select the simplest correct model almost surely if the penalty term increases with model dimension and has an order in between O(log log n) and O(n). 2000 Mathematics Subject Classifications: 62F12, 62J12, 60F15