The Annals of Statistics

A Unified Approach to Improving Equivariant Estimators

Tatsuya Kubokawa

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Abstract

In the point and interval estimation of the variance of a normal distribution with an unknown mean, the best affine equivariant estimators are dominated by Stein's truncated and Brewster and Zidek's smooth procedures, which are separately derived. This paper gives a unified approach to this problem by using a simple definite integral and provides a class of improved procedures in both point and interval estimation of powers of the scale parameter of normal, lognormal, exponential and Pareto distributions. Finally, the same method is applied to the improvement on the James-Stein rule in the simultaneous estimation of a multinormal mean.

Article information

Source
Ann. Statist., Volume 22, Number 1 (1994), 290-299.

Dates
First available in Project Euclid: 11 April 2007

Permanent link to this document
https://projecteuclid.org/euclid.aos/1176325369

Digital Object Identifier
doi:10.1214/aos/1176325369

Mathematical Reviews number (MathSciNet)
MR1272084

Zentralblatt MATH identifier
0816.62021

JSTOR
links.jstor.org

Subjects
Primary: 62C99: None of the above, but in this section
Secondary: 62F11 62F25: Tolerance and confidence regions

Keywords
Point and interval estimation of variance best affine equivariant estimator inadmissibility Brewster-Zidek estimator normal exponential noncentral chi-square distribution simultaneous estimation of multinormal mean James-Stein rule

Citation

Kubokawa, Tatsuya. A Unified Approach to Improving Equivariant Estimators. Ann. Statist. 22 (1994), no. 1, 290--299. doi:10.1214/aos/1176325369. https://projecteuclid.org/euclid.aos/1176325369


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