## The Annals of Mathematical Statistics

- Ann. Math. Statist.
- Volume 38, Number 6 (1967), 1845-1852.

### On Optimal Asymptotic Tests of Composite Statistical Hypotheses

James B. Bartoo and Prem S. Puri

#### Abstract

A locally asymptotically most powerful test for a composite hypothesis $H:\xi = \xi_0$ has been developed for the case where the observable random variables $\{X_{nk}, k = 1, 2, \cdots, n\}$ are independently but not necessarily identically distributed. However, their distributions depend on $s + 1$ parameters, one being $\xi$ under test and the other being a vector $\theta = (\theta_1, \cdots, \theta_s)$ of nuisance parameters. The theory is illustrated with an example from the field of astronomy.

#### Article information

**Source**

Ann. Math. Statist., Volume 38, Number 6 (1967), 1845-1852.

**Dates**

First available in Project Euclid: 27 April 2007

**Permanent link to this document**

https://projecteuclid.org/euclid.aoms/1177698617

**Digital Object Identifier**

doi:10.1214/aoms/1177698617

**Mathematical Reviews number (MathSciNet)**

MR224206

**Zentralblatt MATH identifier**

0161.37906

**JSTOR**

links.jstor.org

#### Citation

Bartoo, James B.; Puri, Prem S. On Optimal Asymptotic Tests of Composite Statistical Hypotheses. Ann. Math. Statist. 38 (1967), no. 6, 1845--1852. doi:10.1214/aoms/1177698617. https://projecteuclid.org/euclid.aoms/1177698617