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 Teor. Veroyatnost. i Primenen., 2017, Volume 62, Issue 1, Pages 194–211 (Mi tvp5098)

Computable error bounds for high-dimensional approximations of an LR statistic for additional information in canonical correlation analysis

H. Wakaki, Y. Fujikoshi

Department of Mathematical Faculty of Sciences, Hiroshima University, Higashi-Hiroshima, Japan

Abstract: Let $\lambda$ be the LR criterion for testing an additional information hypothesis on a subvector of $p$-variate random vector ${x}$ and a subvector of $q$-variate random vector ${y}$, based on a sample of size $N=n+1$. Using the fact that the null distribution of $-(2/N)\log \lambda$ can be expressed as a product of two independent $\Lambda$ distributions, we first derive an asymptotic expansion as well as the limiting distribution of the standardized statistic $T$ of $-(2/N)\log \lambda$ under a high-dimensional framework when the sample size and the dimensions are large. Next, we derive computable error bounds for the high-dimensional approximations. Through numerical experiments it is noted that our error bounds are useful in a wide range of $p$, $q$, and $n$.

Keywords: error bounds, asymptotic expansions, high-dimensional data, redundancy, canonical correlation analysis.

DOI: https://doi.org/10.4213/tvp5098

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English version:
Theory of Probability and its Applications, 2018, 62:1, 157–172

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Accepted:20.10.2016
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Citation: H. Wakaki, Y. Fujikoshi, “Computable error bounds for high-dimensional approximations of an LR statistic for additional information in canonical correlation analysis”, Teor. Veroyatnost. i Primenen., 62:1 (2017), 194–211; Theory Probab. Appl., 62:1 (2018), 157–172

Citation in format AMSBIB
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• http://mi.mathnet.ru/eng/tvp5098
• https://doi.org/10.4213/tvp5098
• http://mi.mathnet.ru/eng/tvp/v62/i1/p194

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This publication is cited in the following articles:
1. R. Oda, H. Yanagihara, Ya. Fujikoshi, “Asymptotic null and non-null distributions of test statistics for redundancy in high-dimensional canonical correlation analysis”, Random Matrices-Theor. Appl., 8:1 (2019), 1950001
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