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April 1996 Shrinkage estimators, Skorokhod's problem and stochastic integration by parts
Steven N. Evans, Philip B. Stark
Ann. Statist. 24(2): 809-815 (April 1996). DOI: 10.1214/aos/1032894466


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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Steven N. Evans. Philip B. Stark. "Shrinkage estimators, Skorokhod's problem and stochastic integration by parts." Ann. Statist. 24 (2) 809 - 815, April 1996.


Published: April 1996
First available in Project Euclid: 24 September 2002

zbMATH: 0859.62012
MathSciNet: MR1394989
Digital Object Identifier: 10.1214/aos/1032894466

Primary: 62C15 , 62F10

Keywords: Admissibility , balayage , Brownian motion , location parameter , quadratic loss , shift model

Rights: Copyright © 1996 Institute of Mathematical Statistics

Vol.24 • No. 2 • April 1996
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