Rice University

COLLOQUIUM

Department of Statistics

Edward George
University of Texas at Austin

Calibration and Empirical Bayes Variable Selection

Abstract: For the problem of variable selection for the normal linear model, traditional selection criteria such as Cp, AIC and BIC are shown to correspond to hyperparameter choices in a hierarchical Bayes formulation in the sense that model comparison via the criteria can be calibrated exactly to model comparison via posterior probabilities. Maximum marginal likehood estimation within this formulation is then used to derive a new criterion, called the Empirical Bayes Criterion (EBC). EBC is asymptotically consistent and uses the data to adaptively emulate the performance of the optimal criterion across different problems. Finally, for the purpose of estimating the selected coefficients, the empirical Bayes motivation is seen to lead to a highly effective Stein-like shrinkage estimator which mitigates selection bias.

September 22, 1997 at 2:10 P.M.
Duncan Hall CEB 1070 (Gate 16)
Coffee 2:00, Duncan Hall CE1044

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