期刊
ANNALS OF PROBABILITY
卷 41, 期 5, 页码 3284-3305出版社
INST MATHEMATICAL STATISTICS
DOI: 10.1214/12-AOP803
关键词
Negative type; hypothesis testing; independence; distance correlation; Brownian covariance
资金
- NSF [DMS-10-07244]
- Microsoft Research
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 metric spaces and embeddings in Hilbert spaces.
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