## The Annals of Statistics

### The Asymptotic Minimax Character of Sequential Binomial and Sign Tests

Sture Holm

#### 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

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