## The Annals of Statistics

### A Best Sequential Test for Symmetry When the Probability of Termination is Not One

David L. Burdick

#### Abstract

A sequential test of a statistical hypothesis $H_0$ versus $H_1$ is said to be a test of Robbins type if there is a positive probability that the test will not stop if $H_0$ is true. Tests of this nature were introduced for testing the Bernoulli case by Darling and Robbins [1]; an earlier paper of Farrell [2] deals implicitly with the asymptotic expected sample size of such tests for testing the hypothesis $\theta = 0$ in the parametrized family of generalized density functions $h(\theta)e^{\theta x} d\mu$.

#### Article information

Source
Ann. Statist., Volume 1, Number 6 (1973), 1195-1199.

Dates
First available in Project Euclid: 12 April 2007

https://projecteuclid.org/euclid.aos/1176342568

Digital Object Identifier
doi:10.1214/aos/1176342568

Mathematical Reviews number (MathSciNet)
MR368347

Zentralblatt MATH identifier
0295.62048

JSTOR