The Annals of Statistics

The Asymptotic Minimax Character of Sequential Binomial and Sign Tests

Sture Holm

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Abstract

Let $p$ be the probability of any event in repeated independent trials. Sequential tests of the composite hypothesis $p \leqq p_0$ against the composite hypothesis $p > p_0$ are proposed, which asymptotically minimize the maximum risk when the cost of experimentation tends to zero, if the loss depends only on $p$ and satisfies some natural regularity conditions. Asymptotic power, expected sample size and risk of the tests are also given.

Article information

Source
Ann. Statist., Volume 1, Number 6 (1973), 1139-1148.

Dates
First available in Project Euclid: 12 April 2007

Permanent link to this document
https://projecteuclid.org/euclid.aos/1176342562

Digital Object Identifier
doi:10.1214/aos/1176342562

Mathematical Reviews number (MathSciNet)
MR348937

Zentralblatt MATH identifier
0274.62057

JSTOR
links.jstor.org

Keywords
62 45 Sequential tests asymptotically minimax sign test binomial test

Citation

Holm, Sture. The Asymptotic Minimax Character of Sequential Binomial and Sign Tests. Ann. Statist. 1 (1973), no. 6, 1139--1148. doi:10.1214/aos/1176342562. https://projecteuclid.org/euclid.aos/1176342562


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