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A Law of the Iterated Logarithm for the Sample Covariance Matrix

   
@article{ECP1070,
	author = {Steven Sepanski},
	title = {A  Law of the Iterated Logarithm for the Sample Covariance Matrix},
	journal = {Electron. Commun. Probab.},
	fjournal = {Electronic Communications in Probability},
	volume = {8},
	year = {2003},
	keywords = {law of the iterated logarithm, sample covariance, central limit theorem, generalized domain of attraction, multivariate t statistic, extreme values, operator normalization, self normalization},
	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.},
	pages = {no. 7, 63 -76},
	issn = {1083-589X},
	doi = {10.1214/ECP.v8-1070},    
        url = {http://ecp.ejpecp.org/article/view/1070}}