Open Access
June, 1989 Equivariant Estimation in a Model with an Ancillary Statistic
Takeaki Kariya
Ann. Statist. 17(2): 920-928 (June, 1989). DOI: 10.1214/aos/1176347151


This paper reformulates a result of Hora and Buehler on best equivariant estimators to treat a model admitting an ancillary statistic. The approach itself was established by Pitman, Girshick and Savage and Kiefer, and expanded by Zidek. The model considered in this paper is assumed to be generated as an orbit under a group acting on the parameter space. The general result obtained here is applied to a model in the Nile problem, a model with a known variation coefficient, a circle model and the GMANOVA model, and best equivariant estimators (BEE's) are derived. In the first two models, the BEE's dominate the MLE's uniformly.


Download Citation

Takeaki Kariya. "Equivariant Estimation in a Model with an Ancillary Statistic." Ann. Statist. 17 (2) 920 - 928, June, 1989.


Published: June, 1989
First available in Project Euclid: 12 April 2007

zbMATH: 0697.62020
MathSciNet: MR994276
Digital Object Identifier: 10.1214/aos/1176347151

Primary: 62F10
Secondary: 62A05

Keywords: ancillary statistic , best equivariant estimator , circle model , curved model , GMANOVA model , Invariance , MLE , normal model with a known variation coefficient , Sufficient statistic , the Nile problem

Rights: Copyright © 1989 Institute of Mathematical Statistics

Vol.17 • No. 2 • June, 1989
Back to Top