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November 2017 High-dimensional asymptotic distributions of characteristic roots in multivariate linear models and canonical correlation analysis
Yasunori Fujikoshi
Hiroshima Math. J. 47(3): 249-271 (November 2017). DOI: 10.32917/hmj/1509674447

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 $\mathrm{O}(1)$.

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Yasunori Fujikoshi. "High-dimensional asymptotic distributions of characteristic roots in multivariate linear models and canonical correlation analysis." Hiroshima Math. J. 47 (3) 249 - 271, November 2017. https://doi.org/10.32917/hmj/1509674447

Information

Received: 6 May 2016; Revised: 28 September 2016; Published: November 2017
First available in Project Euclid: 3 November 2017

zbMATH: 06836006
MathSciNet: MR3719444
Digital Object Identifier: 10.32917/hmj/1509674447

Subjects:
Primary: 62H10
Secondary: 62E20

Rights: Copyright © 2017 Hiroshima University, Mathematics Program

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Vol.47 • No. 3 • November 2017
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