## Electronic Communications in Probability

### A Weak Law of Large Numbers for the Sample Covariance Matrix

#### 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

Rights
• 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.
• 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.