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 $\mathrm{O}(1)$.
Citation
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
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