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This article is cited in 1 scientific paper (total in 1 paper)
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.
Received: 17.04.2016 Accepted: 20.10.2016
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
Linking options:
https://www.mathnet.ru/eng/tvp5098https://doi.org/10.4213/tvp5098 https://www.mathnet.ru/eng/tvp/v62/i1/p194
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Abstract page: | 313 | Full-text PDF : | 36 | References: | 46 | First page: | 13 |
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