Asymptotic distribution of correlation matrix under blocked compound symmetric covariance structure

IF 0.9 4区数学 Q4 PHYSICS, MATHEMATICAL Random Matrices-Theory and Applications Pub Date : 2021-05-31 DOI:10.1142/S2010326322500162

S. Tsukada

引用次数: 0

Abstract

Assuming a covariance structure with blocked compound symmetry, it was showed that unbiased estimators for the covariance matrices are optimal under normality. In this paper, we derive the asymptotic distribution of the correlation matrix using unbiased estimators and discuss its use in hypothesis testing. The accuracy of the result is investigated through numerical simulation and the method is applied to real data.

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阻塞复合对称协方差结构下相关矩阵的渐近分布

假设一个具有阻塞复合对称的协方差结构，证明了协方差矩阵的无偏估计量在正态性下是最优的。本文利用无偏估计导出了相关矩阵的渐近分布，并讨论了无偏估计在假设检验中的应用。通过数值模拟验证了计算结果的准确性，并将该方法应用于实际数据。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Random Matrices-Theory and Applications Decision Sciences-Statistics, Probability and Uncertainty

CiteScore

1.90

自引率

11.10%

发文量

期刊介绍： Random Matrix Theory (RMT) has a long and rich history and has, especially in recent years, shown to have important applications in many diverse areas of mathematics, science, and engineering. The scope of RMT and its applications include the areas of classical analysis, probability theory, statistical analysis of big data, as well as connections to graph theory, number theory, representation theory, and many areas of mathematical physics. Applications of Random Matrix Theory continue to present themselves and new applications are welcome in this journal. Some examples are orthogonal polynomial theory, free probability, integrable systems, growth models, wireless communications, signal processing, numerical computing, complex networks, economics, statistical mechanics, and quantum theory. Special issues devoted to single topic of current interest will also be considered and published in this journal.