Wilcoxon-type generalized Bayesian information criterion

Lan Wang

Research output: Contribution to journalArticle

15 Scopus citations

Abstract

We develop a generalized Bayesian information criterion for regression model selection. The new criterion relaxes the usually strong distributional assumption associated with Schwarz's bic by adopting a Wilcoxon-type dispersion function and appropriately adjusting the penalty term. We establish that the Wilcoxon-type generalized bic preserves the consistency of Schwarz's bic without the need to assume a parametric likelihood. We also show that it outperforms Schwarz's bic with heavier-tailed data in the sense that asymptotically it can yield substantially smaller L2 risk. On the other hand, when the data are normally distributed, both criteria have similar L2 risk. The new criterion function is convex and can be conveniently computed using existing statistical software. Our proposal provides a flexible yet highly efficient alternative to Schwarz's bic; at the same time, it broadens the scope of Wilcoxon inference, which has played a fundamental role in classical nonparametric analysis.

Original languageEnglish (US)
Pages (from-to)163-173
Number of pages11
JournalBiometrika
Volume96
Issue number1
DOIs
StatePublished - Mar 2009

Keywords

  • Bayesian information criterion
  • Bic
  • Consistency of model selection
  • Heavier-tailed distribution
  • Lrisk
  • Rank
  • Wilcoxon inference

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