On an adjustment of degrees of freedom in the minimum mean squared error estimator

In this paper, we consider an adjustment of degrees of freedom in the minimum mean squared error (MMSE) estimator. We derive the exact MSE of the adjusted MMSE (AMMSE) estimator, and compare the MSE of the AMMSE estimator with those of the Stein-rule (SR), positive-part Stein-rule (PSR) and MMSE estimators by numerical evaluations. It is shown that the adjustment of degrees of freedom is effective when the noncentrality parameter is close to zero, and the MSE performance of the MMSE estimator can be improved in the wide region of the noncentrality parameter by the adjustment. It is also shown that the AMMSE estimator can have the smaller MSE than the PSR estimator in the wide region of the noncentrality parameter.