Shrinkage estimators, Skorokhod's problem and stochastic integration by parts

Abstract

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 d-dimensional shift model is inadmissible under quadratic loss when $d \geq 3$. Our proof involves representing the error distribution as that of a stopped Brownian motion and using elementary stochastic analysis to obtain a generalization of an integration by parts lemma due to Stein in the Gaussian case.