IMPROVING EFFICIENCY OF THE'HKB'ORDINARY TYPE RIDGE ESTIMATOR

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. In this paper, the exact predictive mean squared error of the expanded HKB estimator is derived, and a modified HKB estimator is constructed to be improved in the wide regin of the noncentral parameter. It is also shown that the modified estimator can have a smaller mean squared error than the OLS estimator or the positive-part Stein-rule estimator in the wide region of the noncentral parameter.