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.
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