Draft:Ball covariance

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Instructions · What links here · Ball covariance (talk: + · bio) · (log) · Copyvios report · reFill · Citation Bot · (Search: Google, Bing, Wikipedia) · Submitted 27 days ago by Shushijianke (talk: D · +) · Last edited 0 seconds ago

Ball covariance is a statistical measure that can be used to test the independence of two random variables defined on metric spaces.^[1] The ball covariance is zero if and only if two random variables are independent, making it a good measure of correlation. Its significant contribution lies in proposing an alternative measure of independence in metric spaces. Prior to this, distance covariance in metric spaces^[2] could only detect independence for distance types with strong negative type. However, ball covariance can determine independence for any distance measure.

Ball covariance uses permutation tests to calculate the p-value. This involves first computing the ball covariance for two sets of samples, then comparing this value with many permutation values.

^ Pan, Wenliang; Wang, Xueqin; Zhang, Heping; Zhu, Hongtu; Zhu, Jin (2019-04-11). "Ball Covariance: A Generic Measure of Dependence in Banach Space". Journal of the American Statistical Association. 115 (529): 307–317. doi:10.1080/01621459.2018.1543600. ISSN 0162-1459. PMC 7720858. PMID 33299261.
^ Lyons, Russell (2013-09-01). "Distance covariance in metric spaces". The Annals of Probability. 41 (5). doi:10.1214/12-AOP803. ISSN 0091-1798.

[1] Pan, Wenliang; Wang, Xueqin; Zhang, Heping; Zhu, Hongtu; Zhu, Jin (2019-04-11). "Ball Covariance: A Generic Measure of Dependence in Banach Space". Journal of the American Statistical Association. 115 (529): 307–317. doi:10.1080/01621459.2018.1543600. ISSN 0162-1459. PMC 7720858. PMID 33299261.

[:0-2] Lyons, Russell (2013-09-01). "Distance covariance in metric spaces". The Annals of Probability. 41 (5). doi:10.1214/12-AOP803. ISSN 0091-1798.

[1]

[2]