SHRINKAGE ESTIMATORS, SKOROKHODS PROBLEM AND STOCHASTIC INTEGRATION BY PARTS

For a broad class of error distributions that includes the spherically symmetric ones, we give a short proof that the usual estimator of the mean in a cl-dimensional shift model is inadmissible under quadratic loss when d greater than or equal to 3. Our proof involves representin g the error distribution as that of a stopped Brownian motion and usin g elementary stochastic analysis to obtain a generalization of an inte gration by parts lemma due to Stein in the Gaussian case.