Law of iterated logarithm and consistent model selection criterion in logistic regression
GQ Qian, C Field
STATISTICS & PROBABILITY LETTERS | ELSEVIER SCIENCE BV | Published : 2002
In this paper we establish a law of iterated logarithm for the maximum likelihood estimator of the parameters in a logistic regression model with canonical link. This result establishes the strong consistency of some relevant model selection criteria. For a model selection criterion whose objective function consists of a minus log-likelihood like quantity and a penalty term, we have shown that it will select the simplest correct model almost surely if the penalty term is an increasing function of the model dimension and has an order higher than O(log log n). © 2002 Elsevier Science B.V. All rights reserved.