A Law of the Iterated Logarithm for the Sample Covariance Matrix

Steven J. Sepanski (Saginaw Valley State University)


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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Pages: 63 -76

Publication Date: May 20, 2003

DOI: 10.1214/ECP.v8-1070


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