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January, 1973 An Asymptotically Optimal Sequential Procedure for the Estimation of the Largest Mean
Yung Liang Tong
Ann. Statist. 1(1): 175-179 (January, 1973). DOI: 10.1214/aos/1193342396

Abstract

Interval estimation of the largest mean of $k$ normal populations $(k \geqq 1)$ with a common variance $\sigma^2$ is considered. When $\sigma^2$ is known the optimal fixed-width interval is given so that, to have the probability of coverage uniformly lower bounded by $\gamma$ (preassigned), the sample size needed is minimized. This optimal interval is unsymmetric for $k > 2$. When $\sigma^2$ is unknown a sequential procedure is proposed and its behavior is studied. It is shown that the confidence interval obtained, which is also unsymmetric for $k > 2$, behaves asymptotically as well as the optimal interval. This represents an improvement of the procedure of symmetric intervals considered by the author previously; the improvement is significant, especially when $k$ is large.

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Yung Liang Tong. "An Asymptotically Optimal Sequential Procedure for the Estimation of the Largest Mean." Ann. Statist. 1 (1) 175 - 179, January, 1973. https://doi.org/10.1214/aos/1193342396

Information

Published: January, 1973
First available in Project Euclid: 25 October 2007

zbMATH: 0253.62043
MathSciNet: MR345358
Digital Object Identifier: 10.1214/aos/1193342396

Rights: Copyright © 1973 Institute of Mathematical Statistics

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Vol.1 • No. 1 • January, 1973
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