RESTRICTED LINEAR ESTIMATIONS

In an equality restricted linear model,a necessary and sufficient condition for a linear estimator to be admissible in the set of linear estimators is obtained.Both equality restricted least square and equality restricted ridge estimator are proven to be admissible. In an inequality restricted linear model Y=Xb+e,L’b≥r,where X needs not be a full column rank matrix,the closed form of the general solutions of inequality restricted least square（IRLS）is given.At last,we propose the concept of Inequality restricted ridge estimator（IRRE）,and prove that the IRRE can improve the IRLS very well under some conditions.