Document Type

Article

Publication Date

9-1-1980

Publication Title

Annals of Statistics

Abstract

For a given family F of continuous cdf's n i.i.d. random variables with cdf F∈F are observed sequentially with the object of choosing the largest. An upper bound for the greatest asymptotic probability of choosing the largest is α≐.58, the optimal asymptotic value when F is known, and a lower bound is e−1, the optimal value when the choice is based on ranks. It is known that if F is the family of all normal distributions a minimax stopping rule gives asymptotic probability α of choosing the largest while if F is the family of all uniform distributions a minimax rule gives asymptotic value e−1. This note considers a case intermediate to these extremes.

Volume

8

Issue

5

First Page Number

1171

Last Page Number

1174

DOI

10.1214/aos/1176345156

Included in

Mathematics Commons

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