Regularization in Regression: Comparing Bayesian and Frequentist Methods in a Poorly Informative Situation

Gilles Celeux, Mohammed El Anbari, Jean-Michel Marin and Christian Robert
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Gilles Celeux: Crest
Mohammed El Anbari: Crest
Jean-Michel Marin: Crest
Christian Robert: Crest

No 2010-43, Working Papers from Center for Research in Economics and Statistics

Abstract: We propose a global noninformative approach for Bayesian variable selection that builds onZellner’s g-priors and is similar to Liang et al. (2008). Our proposal does not require any kindof calibration. In the case of a benchmark, we compare Bayesian and frequentist regularizationapproaches under a low informative constraint when the number of variables is almost equalto the number of observations. The simulated and real dataset experiments we present herehighlight the appeal of Bayesian regularization methods, when compared with alternatives.They dominate frequentist methods in the sense they provide smaller prediction errors whileselecting the most relevant variables in a parsimonious way.

Pages: 20
Date: 2010
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