在过去和未来之间的大经验自协方差矩阵的行为

Pub Date : 2019-11-20 DOI:10.1142/s2010326321500210

P. Loubaton, D. Tieplova

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引用次数: 0

摘要

研究了一类高维复高斯不相关序列的样本自协方差矩阵的过去和未来之间的奇异值平方分布的渐近性质。利用高斯工具，建立了该分布表现为一个确定性概率测度，其支持度[公式:见文]被表征。还确定了平方奇异值几乎肯定位于[公式:见文]的邻域中。

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On the behavior of large empirical autocovariance matrices between the past and the future

The asymptotic behavior of the distribution of the squared singular values of the sample autocovariance matrix between the past and the future of a high-dimensional complex Gaussian uncorrelated sequence is studied. Using Gaussian tools, it is established that the distribution behaves as a deterministic probability measure whose support [Formula: see text] is characterized. It is also established that the squared singular values are almost surely located in a neighborhood of [Formula: see text].

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