## The Annals of Statistics

- Ann. Statist.
- Volume 20, Number 1 (1992), 555-561.

### Two-Sided Sequential Tests

Lawrence D. Brown and Eitan Greenshtein

#### Abstract

Let $X_i$ be i.i.d. $X_i \sim F_\theta$. For some parametric families $\{F_\theta\}$, we describe a monotonicity property of Bayes sequential procedures for the decision problem $H_0: \theta = 0$ versus $H_1: \theta \neq 0$. A surprising counterexample is given in the case where $F_\theta$ is $N(\theta, 1)$.

#### Article information

**Source**

Ann. Statist., Volume 20, Number 1 (1992), 555-561.

**Dates**

First available in Project Euclid: 12 April 2007

**Permanent link to this document**

https://projecteuclid.org/euclid.aos/1176348539

**Digital Object Identifier**

doi:10.1214/aos/1176348539

**Mathematical Reviews number (MathSciNet)**

MR1150361

**Zentralblatt MATH identifier**

0774.62085

**JSTOR**

links.jstor.org

**Subjects**

Primary: 62L10: Sequential analysis

Secondary: 62C99: None of the above, but in this section

**Keywords**

Sequential testing total-positivity complete class monotone procedures

#### Citation

Brown, Lawrence D.; Greenshtein, Eitan. Two-Sided Sequential Tests. Ann. Statist. 20 (1992), no. 1, 555--561. doi:10.1214/aos/1176348539. https://projecteuclid.org/euclid.aos/1176348539