Measuring Association between Random Vectors
Methodology
2011-07-25 v1
Abstract
This paper suggests five measures of association between two random vectors X = (X_1, ..., X_p) and Y = (Y_1, ..., Y_q). They are copula based and therefore invariant with respect to the marginal distributions of the components X_i and Y_j. The measures capture positive as well as negative association of X and Y. In case p = q = 1 they reduce to Spearman's rho. Various properties of these new measures are investigated. Nonparametric estimators, based on ranks, for the measures are derived and their small sample behaviour is investigated by simulation. The measures are applied to characterise strength and direction of association of bond and stock indices of five countries over time.
Keywords
Cite
@article{arxiv.1107.4381,
title = {Measuring Association between Random Vectors},
author = {Oliver Grothe and Friedrich Schmid and Julius Schnieders and Johan Segers},
journal= {arXiv preprint arXiv:1107.4381},
year = {2011}
}
Comments
28 pages, 2 figures