DISTANCE MULTIVARIANCE - NEW DEPENDENCE MEASURES FOR RANDOM VECTORS

Publikation: Beitrag in FachzeitschriftForschungsartikelBeigetragenBegutachtung

Beitragende

Abstract

We introduce two new measures for the dependence of n >= 2 random variables: distance multivariance and total distance multivariance. Both measures are based on the weighted L-2-distance of quantities related to the characteristic functions of the underlying random variables. These extend distance covariance (introduced by Szekely, Rizzo and Bakirov) from pairs of random variables to n-tuplets of random variables. We show that total distance multivariance can be used to detect the independence of n random variables and has a simple finite-sample representation in terms of distance matrices of the sample points, where distance is measured by a continuous negative definite function. Under some mild moment conditions, this leads to a test for independence of multiple random vectors which is consistent against all alternatives.

Details

OriginalspracheEnglisch
Seiten (von - bis)2757-2789
Seitenumfang33
FachzeitschriftAnnals of statistics
Jahrgang47
Ausgabenummer5
PublikationsstatusVeröffentlicht - Okt. 2019
Peer-Review-StatusJa

Externe IDs

Scopus 85072197623
ORCID /0000-0003-0913-3363/work/166762745

Schlagworte

Schlagwörter

  • Dependence measure, stochastic independence, negative definite function, characteristic function, Gaussian random field, statistical test of independence, INDEPENDENCE, COVARIANCE