Law of Iterated Logarithm and Strong Consistency in Poisson Regression Model Selection

Authors

  • Guoqi Qian The University of Melbourne

Keywords:

Law of iterated logarithm, Poisson regression, Maximum likelihood estimator, Model selection, Strong consistency.

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 log-likelihood 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 $O(n)$.

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Published

2010-05-22

Issue

Section

Special Issue on Granger Econometrics and Statistical Modeling

How to Cite

Law of Iterated Logarithm and Strong Consistency in Poisson Regression Model Selection. (2010). European Journal of Pure and Applied Mathematics, 3(3), 417-434. https://www.ejpam.com/index.php/ejpam/article/view/515