It is known that the set of correlation coefficients formed from $k$ independent normal samples exhibits pairwise independence of its members (Geisser and Mantel (1962)). Here it is shown that many much larger subsets of the matrix are fully independent. The main result characterises such subsets in a simple way. Because the results are framed in abstract terms, they also apply to rank correlation coefficients and $\chi^2$ statistics.
Publié le : 1987-01-14
Classification:
Correlation matrix,
partial independence,
$\chi^2$ statistics,
distances on metric space,
uniform distribution,
62J15,
60E99,
60G55
@article{1176992279,
author = {Brown, Timothy C.},
title = {Independent Subsets of Correlation and Other Matrices},
journal = {Ann. Probab.},
volume = {15},
number = {4},
year = {1987},
pages = { 416-422},
language = {en},
url = {http://dml.mathdoc.fr/item/1176992279}
}
Brown, Timothy C. Independent Subsets of Correlation and Other Matrices. Ann. Probab., Tome 15 (1987) no. 4, pp. 416-422. http://gdmltest.u-ga.fr/item/1176992279/