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.
Publié le : 1980-04-14
Classification:
Central limit theorem,
truncated correlation,
infinite variance,
matrix normalization,
multivariate normal,
random vectors,
60F05
@article{1176994776,
author = {Hahn, Marjorie G. and Klass, Michael J.},
title = {Matrix Normalization of Sums of Random Vectors in the Domain of Attraction of the Multivariate Normal},
journal = {Ann. Probab.},
volume = {8},
number = {6},
year = {1980},
pages = { 262-280},
language = {en},
url = {http://dml.mathdoc.fr/item/1176994776}
}
Hahn, Marjorie G.; Klass, Michael J. Matrix Normalization of Sums of Random Vectors in the Domain of Attraction of the Multivariate Normal. Ann. Probab., Tome 8 (1980) no. 6, pp. 262-280. http://gdmltest.u-ga.fr/item/1176994776/