Testing Independence Among a Large Number of High-Dimensional Random Vectors
Testing Independence Among a Large Number of High-Dimensional Random Vectors
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DOI：
10.1080/01621459.2013.872037
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发表时间：
2014-04
影响因子：
3.7
通讯作者：
G. Pan;Jiti Gao;Yanrong Yang
中科院分区：
文献类型：
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作者：
G. Pan;Jiti Gao;Yanrong Yang
捕获大量高维随机向量之间的依赖性是一个非常重要且具有挑战性的问题。通过以矩阵的形式排列n个长度为p的随机向量，我们开发了所构造矩阵的线性谱统计量来测试n个随机向量是否独立。具体来说，所提出的统计量也可以应用于 n 个随机向量，每个向量的元素可以写成线性平稳过程或独立随机变量的线性组合。所提出的检验统计量的渐近分布是针对 n → ∞ 的情况建立的。为了避免估计每个随机向量的频谱，构建了一种改进的检验统计量，其基于将原始n个向量分成两个相等的部分并消除包含每个随机向量或时间序列的内部结构的项。极限分布是正态分布并且不需要知道每个研究的随机向量的内部结构的事实导致构造的检验统计量的简单实现。仿真结果表明，所提出的测试对于几种常用的依赖结构来说是强大的。检测 S&P500 中几只股票收盘价依赖性的实证应用也说明了我们提供的测试的适用性和有效性。本文的补充材料可在线获取。
Capturing dependence among a large number of high-dimensional random vectors is a very important and challenging problem. By arranging n random vectors of length p in the form of a matrix, we develop a linear spectral statistic of the constructed matrix to test whether the n random vectors are independent or not. Specifically, the proposed statistic can also be applied to n random vectors, each of whose elements can be written as either a linear stationary process or a linear combination of independent random variables. The asymptotic distribution of the proposed test statistic is established for the case of as n → ∞. To avoid estimating the spectrum of each random vector, a modified test statistic, which is based on splitting the original n vectors into two equal parts and eliminating the term that contains the inner structure of each random vector or time series, is constructed. The facts that the limiting distribution is normal and there is no need to know the inner structure of each investigated random vector result in simple implementation of the constructed test statistic. Simulation results demonstrate that the proposed test is powerful against several commonly used dependence structures. An empirical application to detecting dependence of the closed prices from several stocks in the S&P500 also illustrates the applicability and effectiveness of our provided test. Supplementary materials for this article are available online.