The Annals of Statistics

The Stein Paradox in the Sense of the Pitman Measure of Closeness

Pranab Kumar Sen, Tatsuya Kubokawa, and A. K. Md. Ehsanes Saleh

Full-text: Open access

Abstract

The dominance and related optimality properties of the usual Stein-rule or shrinkage estimators are typically developed for quadratic error loss functions. It is shown that under the classical Pitman closeness criterion the Stein-rule estimators possess a similar dominance property when the "closeness" measure is based on suitable quadratic norms.

Article information

Source
Ann. Statist., Volume 17, Number 3 (1989), 1375-1386.

Dates
First available in Project Euclid: 12 April 2007

Permanent link to this document
https://projecteuclid.org/euclid.aos/1176347276

Digital Object Identifier
doi:10.1214/aos/1176347276

Mathematical Reviews number (MathSciNet)
MR1015158

Zentralblatt MATH identifier
0681.62015

JSTOR
links.jstor.org

Subjects
Primary: 62C15: Admissibility
Secondary: 62H12: Estimation

Keywords
Inadmissibility loss functions Pitman closeness quadratic norm shrinkage estimators Stein phenomenon

Citation

Sen, Pranab Kumar; Kubokawa, Tatsuya; Saleh, A. K. Md. Ehsanes. The Stein Paradox in the Sense of the Pitman Measure of Closeness. Ann. Statist. 17 (1989), no. 3, 1375--1386. doi:10.1214/aos/1176347276. https://projecteuclid.org/euclid.aos/1176347276


Export citation