Open Access
Translator Disclaimer
April, 1971 Admissibility of the Usual Confidence Sets for a Class of Bivariate Populations
V. M. Joshi
Ann. Math. Statist. 42(2): 662-679 (April, 1971). DOI: 10.1214/aoms/1177693416


For a bivariate population, with a probability density $p(|x - \theta|)$ where $p(t)$ is strictly decreasing for $t \geqq 0$, when a single observation is taken, the usual confidence sets are circles of constant radius centered at the observed value. Previous results of Kiefer imply that these circles have the minimax property of minimizing the maximum expected Lebesgue measure of the confidence sets for a given lower confidence level. It is now shown here that subject to mild conditions on $p(t)$, the confidence circles are also essentially unique in having the minimax property. The result generalizes the result proved previously for the bivariate normal case.


Download Citation

V. M. Joshi. "Admissibility of the Usual Confidence Sets for a Class of Bivariate Populations." Ann. Math. Statist. 42 (2) 662 - 679, April, 1971.


Published: April, 1971
First available in Project Euclid: 27 April 2007

zbMATH: 0217.51405
MathSciNet: MR288907
Digital Object Identifier: 10.1214/aoms/1177693416

Rights: Copyright © 1971 Institute of Mathematical Statistics


Vol.42 • No. 2 • April, 1971
Back to Top