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

Vol. 3 No. 3 (2010): Special Issue on Granger Econometrics and Statistical Modeling

Section

Special Issue on Granger Econometrics and Statistical Modeling

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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