J. Japan Statist. Soc., Vol. 31 (No. 1), pp. 67-83, 2001
Abstract. The HKB estimator of Hoerl, Kennard and Baldwin is known to be an ordinary ridge type shrinkage estimator and an adjustment of degrees of freedom in the ordinary ridge estimator of Farebrother. The HKB estimator has a smaller predictive mean squared error (MSE) than the positive-part Stein-rule (PP) estimator in the wide region of the noncentral parameter when the degrees of freedom q = 3 ~ 6, but does not satisfy the sufficient condition to dominate the OLS estimator of Baranchik or Efron and Morris when q = 3. In this paper, a sufficient condition to dominate the OLS estimator is derived, and the modified HKB estimator is constructed to dominate the OLS estimator and have a smaller MSE than the PP estimator in the wide region of the noncentral parameter.
Key words and phrases: ridge regression, MSE dominance condition, HKB estimator, positive-part Stein-rule estimator, predictive mean squared error