James-Stein Estimation

We discuss properties of the James-Stein shrinkage estimator and its relationship to Empirical Bayes in the case of ridge regression and the \(g\)-prior in regression with orthonormal predictors. While the James-Stein and positive-part James-Stein shrinkage estimators dominate the MLE/OLS estimator, they are not admissible.

Readings:

• Christensen Chapter 15

• Seber & Lee Chapter 12

• James and Stein (1961) “Estimation with Quadratic Loss”

• Efron & Morris (1973) “Stein’s Estimation Rule and its Competitors”

• Robert, C. (2007) “The Bayesian Choice” Chapter 5