Electronic Communications in Probability

Electronic Communications in Probability > Vol. 5 (2000) > Paper 8

A Weak Law of Large Numbers for the Sample Covariance Matrix

Steven J. Sepanski, Saginaw Valley State University
Zhidong Pan, Saginaw Valley State University

Abstract
In this article we consider the sample covariance matrix formed from a sequence of independent and identically distributed random vectors from the generalized domain of attraction of the multivariate normal law. We show that this sample covariance matrix, appropriately normalized by a nonrandom sequence of linear operators, converges in probability to the identity matrix.

Full text: PDF

Pages: 73-76

Published on: March 20, 2000

Bibliography

Billingsley, P. (1966) Convergence of types in k-space. Z. Wahrsch. Verw. Gebiete. 5. 175-179. Math Review 33#6665
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Sepanski, S. J. (1994) Asymptotics for multivariate $t$-statistic and Hotelling's $Tsp 2$-statistic under infinite second moments via bootstrapping. J. Multivariate Anal. 49, no. 1, 41--54. Math. Review 96d:62092
Sepanski, Steven J. (1994) Necessary and sufficient conditions for the multivariate bootstrap of the mean. Statist. Probab. Lett. 19 , no. 3, 205--216. Math. Review 95d:62067
Sepanski, Steven J. (1996) Asymptotics for multivariate $t$-statistic for random vectors in the generalized domain of attraction of the multivariate normal law. Statist. Probab. Lett. 30 , no. 2, 179--188. Math. Review 97k:60042

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Electronic Communications in Probability. ISSN: 1083-589X