Infinitely imbalanced binomial regression and deformed exponential families

Tomonari Sei

Research output: Contribution to journalArticle

Abstract

The logistic regression model is known to converge to a Poisson point process model if the binary response tends to infinity 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.

Original languageEnglish
Pages (from-to)116-124
Number of pages9
JournalJournal of Statistical Planning and Inference
Volume149
DOIs
Publication statusPublished - 2014 Jun

Keywords

  • Binomial regression
  • Extreme value theory
  • Imbalanced data
  • Poisson point process
  • Q-Exponential family

ASJC Scopus subject areas

  • Statistics and Probability
  • Statistics, Probability and Uncertainty
  • Applied Mathematics

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