Infinitely imbalanced binomial regression and deformed exponential families

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書誌事項

公開日
2014-06
資源種別
journal article
DOI
  • 10.1016/j.jspi.2014.01.002
  • 10.48550/arxiv.1303.7297
公開者
Elsevier BV

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説明

The logistic regression model is known to converge to a Poisson point process model if the binary response tends to infinitely imbalanced. In this paper, it is shown that this phenomenon is universal in a wide class of link functions on binomial regression. The proof relies on the extreme value theory. For the logit, probit and complementary log-log link functions, the intensity measure of the point process becomes an exponential family. For some other link functions, deformed exponential families appear. A penalized maximum likelihood estimator for the Poisson point process model is suggested.

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