## Hiroshima Mathematical Journal

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

Yasunori Fujikoshi

#### 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
Revised: 28 September 2016
First available in Project Euclid: 3 November 2017

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

#### 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