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首页> 外文期刊>European Physical Journal, H. Historical Perspectives on Contemporary Physics >LIMITING LAWS OF COHERENCE OF RANDOM MATRICES WITH APPLICATIONS TO TESTING COVARIANCE STRUCTURE AND CONSTRUCTION OF COMPRESSED SENSING MATRICES
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LIMITING LAWS OF COHERENCE OF RANDOM MATRICES WITH APPLICATIONS TO TESTING COVARIANCE STRUCTURE AND CONSTRUCTION OF COMPRESSED SENSING MATRICES

机译：随机矩阵的相干性限制律及其在测试方差结构和压缩感知矩阵构建中的应用

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摘要

Testing covariance structure is of significant interest in many areas of statistical analysis and construction of compressed sensing matrices is an important problem in signal processing. Motivated by these applications, we study in this paper the limiting laws of the coherence of an n x p random matrix in the high-dimensional setting where p can be much larger than n. Both the law of large numbers and the limiting distribution are derived. We then consider testing the bandedness of the covariance matrix of a high-dimensional Gaussian distribution which includes testing for independence as a special case. The limiting laws of the coherence of the data matrix play a critical role in the construction of the test. We also apply the asymptotic results to the construction of compressed sensing matrices.
机译：在统计分析的许多领域中，测试协方差结构具有重要意义，而压缩感测矩阵的构造是信号处理中的重要问题。出于这些应用的动机，我们在本文中研究了n维p随机矩阵在高维环境下的相干性的极限定律，其中p可能比n大得多。推导了大数定律和极限分布。然后，我们考虑测试高维高斯分布的协方差矩阵的带度，其中包括作为特殊情况的独立性测试。数据矩阵相干性的限制定律在测试的构建中起着至关重要的作用。我们还将渐近结果应用于压缩感测矩阵的构造。

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