Geodesic
Computable error bounds for high-dimensional approximations of an LR statistic for additional information in canonical correlation analysis
Teoriâ veroâtnostej i ee primeneniâ, Tome 62 (2017) no. 1, pp. 194-211

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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. 
@article{TVP_2017_62_1_a10,
     author = {H. Wakaki and Y. Fujikoshi},
     title = {Computable error bounds for high-dimensional approximations of an {LR} statistic for additional information in canonical correlation analysis},
     journal = {Teori\^a vero\^atnostej i ee primeneni\^a},
     pages = {194--211},
     publisher = {mathdoc},
     volume = {62},
     number = {1},
     year = {2017},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/TVP_2017_62_1_a10/}
}
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H. Wakaki; Y. Fujikoshi. Computable error bounds for high-dimensional approximations of an LR statistic for additional information in canonical correlation analysis. Teoriâ veroâtnostej i ee primeneniâ, Tome 62 (2017) no. 1, pp. 194-211. http://geodesic.mathdoc.fr/item/TVP_2017_62_1_a10/