## Hiroshima Mathematical Journal

- Hiroshima Math. J.
- Volume 47, Number 3 (2017), 249-271.

### High-dimensional asymptotic distributions of characteristic roots in multivariate linear models and canonical correlation analysis

#### Abstract

In this paper, we derive the asymptotic distributions of the characteristic roots in multivariate linear models when the dimension $p$ and the sample size $n$ are large. The results are given for the case that the population characteristic roots have multiplicities greater than unity, and their orders are $\mathrm{O}(np)$ or $\mathrm{O}(n)$. Next, similar results are given for the asymptotic distributions of the canonical correlations when one of the dimensions and the sample size are large, assuming that the order of the population canonical correlations is $\mathrm{O}(\sqrt{p})$ or $\mathrm{O}(1)$.

#### Article information

**Source**

Hiroshima Math. J., Volume 47, Number 3 (2017), 249-271.

**Dates**

Received: 6 May 2016

Revised: 28 September 2016

First available in Project Euclid: 3 November 2017

**Permanent link to this document**

https://projecteuclid.org/euclid.hmj/1509674447

**Digital Object Identifier**

doi:10.32917/hmj/1509674447

**Mathematical Reviews number (MathSciNet)**

MR3719444

**Zentralblatt MATH identifier**

06836006

**Subjects**

Primary: 62H10: Distribution of statistics

Secondary: 62E20: Asymptotic distribution theory

**Keywords**

Asymptotic distributions Canonical correlations Characteristic roots High-dimensional approximations Multivariate linear model

#### Citation

Fujikoshi, Yasunori. High-dimensional asymptotic distributions of characteristic roots in multivariate linear models and canonical correlation analysis. Hiroshima Math. J. 47 (2017), no. 3, 249--271. doi:10.32917/hmj/1509674447. https://projecteuclid.org/euclid.hmj/1509674447