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April, 1980 Matrix Normalization of Sums of Random Vectors in the Domain of Attraction of the Multivariate Normal
Marjorie G. Hahn, Michael J. Klass
Ann. Probab. 8(2): 262-280 (April, 1980). DOI: 10.1214/aop/1176994776

Abstract

Let $S_n$ be a sequence of partial sums of mean zero purely $d$-dimensional i.i.d. random vectors. Necessary and sufficient conditions are given for the existence of matrices $A_n$ such that the transform of $S_n$ by $A_n$ is asymptotically multivariate normal with identity covariance matrix. This is more general than previous $d$-dimensional results. Examples are given to illustrate the need for the present approach. The matrices $A_n$ take a particularly simple form because of a degree of uncorrelatedness between certain pairs of 1-dimensional random variables obtained by projection.

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Marjorie G. Hahn. Michael J. Klass. "Matrix Normalization of Sums of Random Vectors in the Domain of Attraction of the Multivariate Normal." Ann. Probab. 8 (2) 262 - 280, April, 1980. https://doi.org/10.1214/aop/1176994776

Information

Published: April, 1980
First available in Project Euclid: 19 April 2007

zbMATH: 0428.60032
MathSciNet: MR566593
Digital Object Identifier: 10.1214/aop/1176994776

Subjects:
Primary: 60F05

Rights: Copyright © 1980 Institute of Mathematical Statistics

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Vol.8 • No. 2 • April, 1980
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