Asymptotic null and non-null distributions of test statistics for redundancy in high-dimensional canonical correlation analysis
Asymptotic null and non-null distributions of test statistics for redundancy in high-dimensional canonical correlation analysis
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DOI：
10.1142/s2010326319500011
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发表时间：
2018
期刊：
影响因子：
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通讯作者：
Ryoya Oda;H. Yanagihara;Y. Fujikoshi
中科院分区：
文献类型：
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作者：
Ryoya Oda;H. Yanagihara;Y. Fujikoshi
在本文中，我们得出了三个测试统计量的渐近无效和非零用分布，即，可能性比标准，Lawley-hotelling Criterion和Bartlett-Nanda-Pillai标准，用于高度（HD）（HD）的测试（HD） ）规范相关性分析。 [公式：参见文本]和[0,1中的正常常数），以评估不对称分布，这表明我们所提出的HD近似值比经典的不对称框架更准确样本量倾向于[公式：参见文本]。
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 [Formula: see text] 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 [Formula: see text].