Distance covariance in metric spaces

  title={Distance covariance in metric spaces},
  author={Russell Lyons},
  journal={Annals of Probability},
  • R. Lyons
  • Published 28 June 2011
  • Mathematics
  • Annals of Probability
We extend the theory of distance (Brownian) covariance from Euclidean spaces, where it was introduced by Szekely, 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… Expand
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