## The Annals of Statistics

### An Asymptotic Expansion of the Nonnull Distribution of Wilks Criterion for Testing the Multivariate Linear Hypothesis

#### Abstract

An asymptotic expansion of the nonnull distribution of the Wilks statistic for testing the linear hypothesis in multivariate analysis of variance is obtained up to the order $N^{-2}$ where $N$ is the sample size, for the first time in terms of noncentral beta distributions. The asymptotic distributions are better than the ones available in Anderson (1958) in the null case and in Sugiura and Fujikoshi (1969) and Posten and Bergman (1964) in the nonnull case. In fact, for certain parameters the asymptotic expansion reduces to the first term and we get the exact distribution.

#### Article information

Source
Ann. Statist., Volume 12, Number 4 (1984), 1576-1583.

Dates
First available in Project Euclid: 12 April 2007

Permanent link to this document
https://projecteuclid.org/euclid.aos/1176346816

Digital Object Identifier
doi:10.1214/aos/1176346816

Mathematical Reviews number (MathSciNet)
MR760712

Zentralblatt MATH identifier
0554.62016

JSTOR
links.jstor.org

Subjects
Primary: 62H10: Distribution of statistics
Secondary: 62E20: Asymptotic distribution theory 62H15: Hypothesis testing

#### Citation

Kulp, R. W.; Nagarsenker, B. N. An Asymptotic Expansion of the Nonnull Distribution of Wilks Criterion for Testing the Multivariate Linear Hypothesis. Ann. Statist. 12 (1984), no. 4, 1576--1583. doi:10.1214/aos/1176346816. https://projecteuclid.org/euclid.aos/1176346816