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Medientyp:
E-Artikel
Titel:
DISTANCE COVARIANCE IN METRIC SPACES
Beteiligte:
Lyons, Russell
Erschienen:
Institute of Mathematical Statistics, 2013
Erschienen in:The Annals of Probability
Sprache:
Englisch
DOI:
10.1214/12-AOP803
ISSN:
0091-1798
Entstehung:
Anmerkungen:
Beschreibung:
<p>We extend the theory of distance (Brownian) covariance from Euclidean spaces, where it was introduced by Székely, Rizzo and Bakirov, to general metric spaces. We show that for testing independence, it is necessary and sufficient that the metric space be of strong negative type. In particular, we show that this holds for separable Hubert spaces, which answers a question of Kosorok. Instead of the manipulations of Fourier transforms used in the original work, we use elementary inequalities for metric spaces and embeddings in Hubert spaces.</p>