## The Annals of Statistics

- Ann. Statist.
- Volume 6, Number 3 (1978), 546-558.

### Exact Slopes of Certain Multivariate Tests of Hypotheses

#### Abstract

Bahadur and Raghavachari have formulated the likelihood ratio method of finding the exact slope of a sequence of test statistics which does not require explicit estimation of large deviation probabilities. The method is described herein, and readily verifiable conditions under which it may be invoked are given. The method is then used to find the exact slopes of certain sequences of test statistics arising in multivariate analysis.

#### Article information

**Source**

Ann. Statist., Volume 6, Number 3 (1978), 546-558.

**Dates**

First available in Project Euclid: 12 April 2007

**Permanent link to this document**

https://projecteuclid.org/euclid.aos/1176344199

**Digital Object Identifier**

doi:10.1214/aos/1176344199

**Mathematical Reviews number (MathSciNet)**

MR484699

**Zentralblatt MATH identifier**

0386.62035

**JSTOR**

links.jstor.org

**Subjects**

Primary: 62F20

Secondary: 62H15: Hypothesis testing 62F05: Asymptotic properties of tests

**Keywords**

Bahadur efficiency exact slope likelihood ratio method multivariate tests

#### Citation

Koziol, James A. Exact Slopes of Certain Multivariate Tests of Hypotheses. Ann. Statist. 6 (1978), no. 3, 546--558. doi:10.1214/aos/1176344199. https://projecteuclid.org/euclid.aos/1176344199