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Abstract : |
For the problem ofvariable selection for the normal linear model, selection criteria such as AIC, Cp, BIC and RIC have fixed dimensionality penalties. Such criteria are shown to correspond to selection ofmaximum posterior models under implicit hyperparameter choices for a particular hierarchical Bayes formulation. Based on this calibration, we propose empirical Bayes selection criteria that use hyperparameter estimates instead offixed choices. For obtaining these estimates, both marginal and conditional maximum likelihood methods are considered. As opposed to traditional fixed penalty criteria, these empirical Bayes criteria have dimensionality penalties that depend on the data. Their performance is seen to approximate adaptively the performance ofthe best fixed penalty criterion across a variety oforthogonal and nonorthogonal set-ups, including wavelet regression. Empirical Bayes shrinkage estimators ofthe selected coefficients are also proposed., |
