Bayes and Empirical Bayes Shrinkage Estimation of Regression Coefficients: A Cross-Validation Study

Abstract

A Bayesian and an empirical Bayes approach to shrinkage estimation of regression coefficients and the uses of these in prediction are investigated. The methods, along with least squares and least absolute deviations, are applied to data sets of different sizes and cross-validated with observations not in the data sets. The fully Bayes and empirical Bayes methods are seen to perform consistently better in predicting the response variable than either of least squares or least absolute deviations.