The Annals of Mathematical Statistics

Noncentral Distribution of Wilks' Statistic in Manova

A. K. Gupta

Full-text: Open access

Abstract

In this paper, the exact distribution of Wilks' likelihood ratio criterion, $\Lambda$, for MANOVA in the noncentral linear case i.e. when the alternative hypothesis is of unit rank, has been obtained and explicit expressions for the same for $p = 2, 3, 4$ and 5, where $p$ is the number of variables and for general $f_1$ and $f_2$ are given. A general form of the distribution of $\Lambda$ in this case, for any $p$, is also given. It has been shown that the total integral of the series obtained by taking a few terms only, rapidly approaches the theoretical value one as more terms are taken into account. Further the accuracy of the approximation, suggested by Posten and Bargmann [11], is examined numerically and it has been shown that the approximation is excellent except when $f_1$ and $f_2$ are both small and the noncentrality parameter $\lambda^2$ is large.

Article information

Source
Ann. Math. Statist., Volume 42, Number 4 (1971), 1254-1261.

Dates
First available in Project Euclid: 27 April 2007

Permanent link to this document
https://projecteuclid.org/euclid.aoms/1177693238

Digital Object Identifier
doi:10.1214/aoms/1177693238

Mathematical Reviews number (MathSciNet)
MR292226

Zentralblatt MATH identifier
0223.62064

JSTOR
links.jstor.org

Citation

Gupta, A. K. Noncentral Distribution of Wilks' Statistic in Manova. Ann. Math. Statist. 42 (1971), no. 4, 1254--1261. doi:10.1214/aoms/1177693238. https://projecteuclid.org/euclid.aoms/1177693238


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