CHEN Minqiong, . Two Notes on Energy Distance[J]. Chinese Journal of Applied Probability and Statistics, 2018, 34(5): 463-474.
Citation: CHEN Minqiong, . Two Notes on Energy Distance[J]. Chinese Journal of Applied Probability and Statistics, 2018, 34(5): 463-474.

Two Notes on Energy Distance

Funds: The project was supported by the Natural Science Foundation of Guangdong Province for Young Innovative Talents (Grant No. 2014KQNCX253).
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  • Corresponding author:

    CHEN Minqiong, E-mail: C_skirt@163.com

  • The definition of Brownian distance is presented and it's proved that Brownian distance coincides with the energy distance with respect to Brownian motion. Energy distance for dependent random vectors is also given and the asymptotic distribution is derived under null hypothesis. A simple numerical simulation result shows that the method for paired-sample test based on energy distance can distinguish the distributions of the paired variables more effectively than the classical t-test and Wilcoxon signed rank test.
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