SOME MODIFICATIONS OF IMPROVED ESTIMATORS OF A NORMAL VARIANCE

Consider the problem of estimating a normal variance based on a random sample when the mean is unknown. Scale equivariant estimators which i mprove upon the best scale and translation equivariant one have been p roposed by several authors for various loss functions including quadra tic loss. However, at least for quadratic loss function, improvement i s not much. Herein, some methods are proposed to construct improving e stimators which are not scale equivariant and are expected to be consi derably better when the true variance value is close to the specified one. The idea behind the methods is to modify improving equivariant sh rinkage estimators, so that the resulting ones shrink little when the usual estimate is less than the specified value and shrink much more o therwise. Sufficient conditions are given for the estimators to domina te the best scale and translation equivariant rule under the quadratic loss and the entropy loss. Further, some results of a Monte Carlo exp eriment are reported which show the significant improvements by the pr oposed estimators.