Optimal Confidence Interval for a Ranked Parameter
- 1 September 1973
- journal article
- research article
- Published by JSTOR in Journal of the American Statistical Association
- Vol. 68 (343) , 720
- https://doi.org/10.2307/2284806
Abstract
There are given k univariate distributions, indexed by a real-valued parameter θ, and k independent observations, one from each distribution. Let θ* denote the largest among the values of θ associated with the given distributions. This article is concerned with the estimation of θ*. A class of confidence intervals and a subclass of “optimal” confidence intervals for θ* are given. For a general class of distributions it is shown that the coverage probability of the confidence intervals is minimized for a specified configuration of the set of admissible values of θ.Keywords
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