The Annals of Statistics

A Unified Approach to Improving Equivariant Estimators

Tatsuya Kubokawa

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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

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

First available in Project Euclid: 11 April 2007

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Zentralblatt MATH identifier


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

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


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

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