Empirical Bayes methods are shown to provide a practical alternative to standard least squares methods in fitting high dimensional models to sparse data. An example concerning prediction bias in educational testing is presented as an illustration. (Author)

Classical statistical methods and the small enrollments in graduate departments have constrained the Graduate Record Examinations (GRE) Validity Study Service to providing only validities for single predictors. Estimates of the validity of two or more predictors, used jointly, are considered too unreliable because the corresponding prediction…