Testing for independence of large dimensional vectors
高维向量独立性的检验AI 解读 ↓
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AI 根据所提供的论文材料归类：摘要研究一般高维向量的独立性及随机矩阵检验，未指向所列具体经济计量领域。
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高维向量独立性的检验
- 研究问题
- 当两个向量的维度随样本量增长且维度可能不平衡时，如何检验其独立性，并评估检验水平与不同相关结构下的功效？
- 方法与思路
- 作者针对分块对角协方差原假设提出多元方差分析型统计量，借助随机矩阵理论研究中心及条件非中心 Fisher 矩阵的线性谱统计量。
- 材料陈述的贡献
- 摘要称，新检验在部分维度不平衡情形下较好维持名义水平，且其中一个检验在所考察的多种相关情景中表现出最高功效。
- 阅读关注点
- 应核对协方差分块对角与独立性等价所需条件、维度增长比例，以及非中心谱统计量理论和模拟比较的具体适用范围。
- 阅读边界
- 仅据稿件版本未注明的 OpenAlex 索引摘要；独立性所需分布条件与模拟数值未说明，不能将有限情景的功效比较解释为普遍优越。
原文摘要
In this paper, new tests for the independence of two high-dimensional vectors are investigated. We consider the case where the dimension of the vectors increases with the sample size and propose multivariate analysis of variance-type statistics for the hypothesis of a block diagonal covariance matrix. The asymptotic properties of the new test statistics are investigated under the null hypothesis and the alternative hypothesis using random matrix theory. For this purpose, we study the weak convergence of linear spectral statistics of central and (conditionally) noncentral Fisher matrices. In particular, a central limit theorem for linear spectral statistics of large dimensional (conditionally) noncentral Fisher matrices is derived which is then used to analyse the power of the tests under the alternative. The theoretical results are illustrated by means of a simulation study where we also compare the new tests with several alternative, in particular with the commonly used corrected likelihood ratio test. It is demonstrated that the latter test does not keep its nominal level, if the dimension of one sub-vector is relatively small compared to the dimension of the other sub-vector. On the other hand, the tests proposed in this paper provide a reasonable approximation of the nominal level in such situations. Moreover, we observe that one of the proposed tests is most powerful under a variety of correlation scenarios.