Electronic Communications in Probability

A Law of the Iterated Logarithm for the Sample Covariance Matrix

Steven Sepanski

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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.

Article information

Source
Electron. Commun. Probab., Volume 8 (2003), paper no. 7, 63-76.

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

Permanent link to this document
https://projecteuclid.org/euclid.ecp/1463608891

Digital Object Identifier
doi:10.1214/ECP.v8-1070

Mathematical Reviews number (MathSciNet)
MR1987095

Zentralblatt MATH identifier
1061.60028

Subjects
Primary: 60F15: Strong theorems
Secondary: 60F05: Central limit and other weak theorems

Keywords
law of the iterated logarithm sample covariance central limit theorem generalized domain of attraction multivariate t statistic extreme values operator normalization self normalization

Rights
This work is licensed under aCreative Commons Attribution 3.0 License.

Citation

Sepanski, Steven. A Law of the Iterated Logarithm for the Sample Covariance Matrix. Electron. Commun. Probab. 8 (2003), paper no. 7, 63--76. doi:10.1214/ECP.v8-1070. https://projecteuclid.org/euclid.ecp/1463608891


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