Distance Covariance in Metric Spaces

Details Distance Covariance in Metric Spaces Distance Covariance in Metric Spaces

2011-06-28

arxiv.org/abs/1106.5758v3

Mathematics

Statistics Theory

22 pages

Scientific paper

We extend the theory of distance (Brownian) covariance from Euclidean spaces, where it was introduced by Sz\'ekely, 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 Hilbert 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 Hilbert spaces.

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