Abstract

For a random sample of n iid p-dimensional vectors, each partitioned into b sub-vectors of dimensions p_i, $i=1,\dots ,b,$ tests for zero correlation of sub-vectors are presented when $p_i\gg n$ and the distribution need not be normal. The test statistics are composed of U-statistics based estimators of the Frobenius norm measuring the distance between the null and alternative hypotheses. Asymptotic distributions of the tests are provided for $n,p_i\to \infty ,$ with their finite-sample performance demonstrated through simulations. Some related tests are discussed. A real data application is also given.

中文翻译：

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一些大维向量的相关性检验

摘要

对于n iid p维向量的随机样本，每个向量被划分为b个维度为p _i的子向量，$我=\mathrm{1个},\dots \dots ,b,$子向量的零相关性测试出现在$p_{我}\gg n$并且分布不必是正常的。检验统计量由基于U统计量的 Frobenius 范数估计量组成，用于测量原假设和替代假设之间的距离。提供了测试的渐近分布$n,p_{我}\to \infty ,$通过模拟证明了它们的有限样本性能。讨论了一些相关的测试。还给出了一个真实的数据应用。