The Choice Of Parameters. Ling And Pan Ling Estimated Improvements, Estimated Stein Of The Sls

As for the determination of parameter in ridge estimator,the author gives a new successive iteration method to determine ridge parameter k.The mean square error of ridge estimator can be decreased by means of changing ridge parameter.The method has improved the Hoerl-Kennard formula.In the light of the essence of the ill condition in the linear regression model,and by means of combining some famous classes of estimators so as to improve the exiting classes of estimators,this paper first proposes the c-(K,S)class of estimators of the coefficients,which combines the universal ridge regression estimators and the Stein shrinkage estimators into a bigger class of estimators.The universal ridge estimation is improved by applying the idea of James-Stein regression on this class of biased estimation, and the condition the optimal value of the parameter satisfies is given.Then the optimal value of the parameter is examined and each of its upper bounds and lower bounds is given respectively.At the same time,further research on the c-(K,S)class of estimators of the coefficients is done.It is proved that under the mean square error criterion the Stein estimators can be improved via universal ridge estimator technique and the condition the optimal value of the parameter satisfies is given.The method proposed in this paper provides a technical way to the improvement of the biased estimation.