Bayesian and Frequentist Risk

We study frequentist properties of Bayes estimators of the regression coefficients under the \(g\)-prior and independent normal prior that leads to ridge regression. In particular, there are values of the hper-parameters in the prior that lead to Bayes estimators dominating OLS in terms of MSE.

Readings:

• Christensen Chapter 2.9 and Chapter 15

• Seber & Lee Chapter 3.12, 10.7.3 and 12

• Hoerl, A.E. and Kennard, R.W. (1970) Ridge regression: Biased estimation for nonorthogonal problems. Technometrics, 12(1):55–67

• Zellner, A. (1986) On assessing prior distributions and Bayesian regression analysis with \(g\)-prior distributions. In Bayesian Inference and Decision Techniques: Essays in Honor of Bruno de Finetti, eds. P. K. Goel and A. Zellner, 233–243. Amsterdam: North-Holland