## The Annals of Statistics

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

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

#### 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

**Permanent link to this document**

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**

links.jstor.org

**Subjects**

Primary: 62N15

Secondary: 62G10: Hypothesis testing 62G20: Asymptotic properties

#### Citation

Burdick, David L. A Best Sequential Test for Symmetry When the Probability of Termination is Not One. Ann. Statist. 1 (1973), no. 6, 1195--1199. doi:10.1214/aos/1176342568. https://projecteuclid.org/euclid.aos/1176342568