## The Annals of Statistics

### An Asymptotically Optimal Sequential Procedure for the Estimation of the Largest Mean

Yung Liang Tong

#### 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.

#### Article information

Source
Ann. Statist., Volume 1, Number 1 (1973), 175-179.

Dates
First available in Project Euclid: 25 October 2007

https://projecteuclid.org/euclid.aos/1193342396

Digital Object Identifier
doi:10.1214/aos/1193342396

Mathematical Reviews number (MathSciNet)
MR345358

Zentralblatt MATH identifier
0253.62043

#### Citation

Tong, Yung Liang. An Asymptotically Optimal Sequential Procedure for the Estimation of the Largest Mean. Ann. Statist. 1 (1973), no. 1, 175--179. doi:10.1214/aos/1193342396. https://projecteuclid.org/euclid.aos/1193342396