## The Annals of Mathematical Statistics

- Ann. Math. Statist.
- Volume 40, Number 3 (1969), 942-952.

### Asymptotic Expansions of the Non-Null Distributions of the Likelihood Ratio Criteria for Multivariate Linear Hypothesis and Independence

Nariaki Sugiura and Yasunori Fujikoshi

#### Abstract

Asymptotic non-null distribution of the likelihood ratio criterion for testing the linear hypothesis in multivariate analysis is obtained up to the order $N^{-2}$, where $N$ means the sample size, by using the characteristic function expressed in terms of hypergeometric function with matrix argument. This result holds without any assumption on the rank of non-centrality matrix. Asymptotic non-null distribution of the likelihood ratio criterion for independence between two sets of variates is also obtained up to the order $N^{-1}$.

#### Article information

**Source**

Ann. Math. Statist., Volume 40, Number 3 (1969), 942-952.

**Dates**

First available in Project Euclid: 27 April 2007

**Permanent link to this document**

https://projecteuclid.org/euclid.aoms/1177697599

**Digital Object Identifier**

doi:10.1214/aoms/1177697599

**Mathematical Reviews number (MathSciNet)**

MR250401

**Zentralblatt MATH identifier**

0184.22303

**JSTOR**

links.jstor.org

#### Citation

Sugiura, Nariaki; Fujikoshi, Yasunori. Asymptotic Expansions of the Non-Null Distributions of the Likelihood Ratio Criteria for Multivariate Linear Hypothesis and Independence. Ann. Math. Statist. 40 (1969), no. 3, 942--952. doi:10.1214/aoms/1177697599. https://projecteuclid.org/euclid.aoms/1177697599