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Law of iterated logarithm and consistent model selection criterion in logistic regression

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  • Qian, Guoqi
  • Field, Chris
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    Abstract

    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(loglog n).

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    Bibliographic Info

    Article provided by Elsevier in its journal Statistics & Probability Letters.

    Volume (Year): 56 (2002)
    Issue (Month): 1 (January)
    Pages: 101-112

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    Handle: RePEc:eee:stapro:v:56:y:2002:i:1:p:101-112

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    Related research

    Keywords: Law of the iterated logarithm Logistic regression Maximum likelihood estimator Model selection Strong consistency;

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    Cited by:
    1. Jin, Man & Fang, Yixin & Zhao, Lincheng, 2005. "Variable selection in generalized linear models with canonical link functions," Statistics & Probability Letters, Elsevier, vol. 71(4), pages 371-382, March.
    2. Guoqi Qian & Yuehua Wu & Qing Shao, 2009. "A Procedure for Estimating the Number of Clusters in Logistic Regression Clustering," Journal of Classification, Springer, vol. 26(2), pages 183-199, August.
    3. Eva Cantoni & Chris Field & Joanna Mills Flemming & Elvezio Ronchetti, 2005. "Longitudinal variable selection by cross-validation in the case of many covariates," Research Papers by the Institute of Economics and Econometrics, Geneva School of Economics and Management, University of Geneva 2005.01, Institut d'Economie et Econométrie, Université de Genève.

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