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Biometrika Advance Access originally published online on January 22, 2009
Biometrika 2009 96(1):163-173; doi:10.1093/biomet/asn060
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© 2009 Biometrika Trust

Articles

Wilcoxon-type generalized Bayesian information criterion

Lan Wang

School of Statistics, University of Minnesota, 313 Ford Hall, 224 Church Street S.E., Minneapolis, Minnesota 55455, U.S.A. lan{at}stat.umn.edu

Received for publication 1 June 2007. Revision received 1 June 2008.
  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.

Key Words: BIC • Bayesian information criterion • Consistency of model selection • Heavier-tailed distribution • L2 risk • Rank • Wilcoxon inference


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