Asymptotic Probabilities of Over-estimating and Under-estimating the Order of a Model in General Regular Families

Abstract

Large and moderate deviation principles are applied to find the limiting behavior of the probability of under-estimating or over-estimating the order of a model when using a maximum penalized likelihood estimator. The models are assumed to be identifiable even if the order is over-estimated. This paper extends known results concerning models in exponential families to more general regular models. Applications using negative binomial distributions are given.

Keywords:

• Penalized maximum likelihood
• Large deviations
• Moderate deviations
• Information criteria
• Model selection
• Negative binomial distributions