## The Annals of Statistics

### 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.

#### Article information

Source
Ann. Statist., Volume 24, Number 2 (1996), 809-815.

Dates
First available in Project Euclid: 24 September 2002

https://projecteuclid.org/euclid.aos/1032894466

Digital Object Identifier
doi:10.1214/aos/1032894466

Mathematical Reviews number (MathSciNet)
MR1394989

Zentralblatt MATH identifier
0859.62012

Subjects
Primary: 62C15: Admissibility 62F10: Point estimation

#### Citation

Evans, Steven N.; Stark, Philip B. Shrinkage estimators, Skorokhod's problem and stochastic integration by parts. Ann. Statist. 24 (1996), no. 2, 809--815. doi:10.1214/aos/1032894466. https://projecteuclid.org/euclid.aos/1032894466

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