Shrinkage estimators, Skorokhod's problem and stochastic integration by parts
Steven N. Evans and Philip B. Stark
Source: Ann. Statist. Volume 24, Number 2
(1996), 809-815.
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.
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Permanent link to this document: http://projecteuclid.org/euclid.aos/1032894466
Mathematical Reviews number (MathSciNet): MR1394989
Digital Object Identifier: doi:10.1214/aos/1032894466
Zentralblatt MATH identifier: 0859.62012
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