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- Title
Asymptotic null and non-null distributions of test statistics for redundancy in high-dimensional canonical correlation analysis.
- Authors
Oda, Ryoya; Yanagihara, Hirokazu; Fujikoshi, Yasunori
- Abstract
In this paper, we derive asymptotic null and non-null distributions of three test statistics, namely, the likelihood ratio criterion, the Lawley–Hotelling criterion, and the Bartlett–Nanda–Pillai criterion, for tests of redundancy in high-dimensional (HD) canonical correlation analysis. Since our setting is that the dimension of one of two observation vectors may be large but does not exceed the sample size, we use a HD asymptotic framework such that the sample size and the dimension divided by the sample size tend to ∞ and a positive constant within [0,1), respectively, for evaluating asymptotic distributions. Through simulation experiments, it is shown that our proposed HD approximations are more accurate than those under the classical asymptotic framework, i.e. only the sample size tends to ∞.
- Subjects
LINEAR free energy relationship; APPROXIMATION theory; FUNCTIONAL analysis; MATHEMATICAL functions; POLYNOMIALS
- Publication
Random Matrices: Theory & Application, 2019, Vol 8, Issue 1, pN.PAG
- ISSN
2010-3263
- Publication type
Article
- DOI
10.1142/S2010326319500011