Electronic Communications in Probability

A Weak Law of Large Numbers for the Sample Covariance Matrix

Steven Sepanski and Zhidong Pan

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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.

Article information

Source
Electron. Commun. Probab., Volume 5 (2000), paper no. 8, 73-76.

Dates
Accepted: 20 March 2000
First available in Project Euclid: 2 March 2016

Permanent link to this document
https://projecteuclid.org/euclid.ecp/1456943501

Digital Object Identifier
doi:10.1214/ECP.v5-1020

Mathematical Reviews number (MathSciNet)
MR1781840

Zentralblatt MATH identifier
0954.60012

Subjects
Primary: 60F05: Central limit and other weak theorems
Secondary: 62E20: Asymptotic distribution theory 62H12: Estimation

Keywords
Law of large numbers affine normalization samplecovariance central limit theorem domain of attraction generalized domain of attraction multivariate t statistic

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

Citation

Sepanski, Steven; Pan, Zhidong. A Weak Law of Large Numbers for the Sample Covariance Matrix. Electron. Commun. Probab. 5 (2000), paper no. 8, 73--76. doi:10.1214/ECP.v5-1020. https://projecteuclid.org/euclid.ecp/1456943501


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References

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