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.
@article{1032894466,
author = {Evans, Steven N. and Stark, Philip B.},
title = {Shrinkage estimators, Skorokhod's problem and stochastic integration by parts},
journal = {Ann. Statist.},
volume = {24},
number = {6},
year = {1996},
pages = { 809-815},
language = {en},
url = {http://dml.mathdoc.fr/item/1032894466}
}
Evans, Steven N.; Stark, Philip B. Shrinkage estimators, Skorokhod's problem and stochastic integration by parts. Ann. Statist., Tome 24 (1996) no. 6, pp. 809-815. http://gdmltest.u-ga.fr/item/1032894466/