Energy statistics: A class of statistics based on distances

Energy distance is a statistical distance between the distributions of random vectors, which characterizes equality of distributions. The name energy derives from Newton's gravitational potential energy, and there is an elegant relation to the notion of potential energy between statistical obse...

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Bibliographic Details
Published in:Journal of statistical planning and inference 2013-08, Vol.143 (8), p.1249-1272
Main Authors: Székely, Gábor J., Rizzo, Maria L.
Format: Article
Language:English
Subjects:
Distance correlation
Distance covariance
Energy distance
Goodness-of-fit
Multivariate independence
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Summary:Energy distance is a statistical distance between the distributions of random vectors, which characterizes equality of distributions. The name energy derives from Newton's gravitational potential energy, and there is an elegant relation to the notion of potential energy between statistical observations. Energy statistics are functions of distances between statistical observations in metric spaces. Thus even if the observations are complex objects, like functions, one can use their real valued nonnegative distances for inference. Theory and application of energy statistics are discussed and illustrated. Finally, we explore the notion of potential and kinetic energy of goodness-of-fit.
ISSN:0378-3758
1873-1171
DOI:10.1016/j.jspi.2013.03.018