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- W2964719927 abstract "We introduce two new measures for the dependence of $nge2$ random variables: distance multivariance and total distance multivariance. Both measures are based on the weighted $L^{2}$-distance of quantities related to the characteristic functions of the underlying random variables. These extend distance covariance (introduced by Székely, Rizzo and Bakirov) from pairs of random variables to $n$-tuplets of random variables. We show that total distance multivariance can be used to detect the independence of $n$ random variables and has a simple finite-sample representation in terms of distance matrices of the sample points, where distance is measured by a continuous negative definite function. Under some mild moment conditions, this leads to a test for independence of multiple random vectors which is consistent against all alternatives." @default.
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- W2964719927 date "2019-10-01" @default.
- W2964719927 modified "2023-10-14" @default.
- W2964719927 title "Distance multivariance: New dependence measures for random vectors" @default.
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- W2964719927 doi "https://doi.org/10.1214/18-aos1764" @default.
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