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2003 A Law of the Iterated Logarithm for the Sample Covariance Matrix
Steven Sepanski
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Electron. Commun. Probab. 8: 63-76 (2003). DOI: 10.1214/ECP.v8-1070

Abstract

For a sequence of independent identically distributed Euclidean random vectors, we prove a law of the iterated logarithm for the sample covariance matrix when $o(\log \log n)$ terms are omitted. The result is proved under the hypothesis that the random vectors belong to the generalized domain of attraction of the multivariate Gaussian law. As an application, we obtain a bounded law of the iterated logarithm for the multivariate t-statistic.

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Steven Sepanski. "A Law of the Iterated Logarithm for the Sample Covariance Matrix." Electron. Commun. Probab. 8 63 - 76, 2003. https://doi.org/10.1214/ECP.v8-1070

Information

Accepted: 20 May 2003; Published: 2003
First available in Project Euclid: 18 May 2016

zbMATH: 1061.60028
MathSciNet: MR1987095
Digital Object Identifier: 10.1214/ECP.v8-1070

Subjects:
Primary: 60F15
Secondary: 60F05

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