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 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.

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  1. Hernández-Lobato, Daniel; Morales-Mombiela, Pablo; Lopez-Paz, David; Suárez, Alberto: Non-linear causal inference using Gaussianity measures (2016)
  2. Nuno Fachada, Joao Rodrigues, Vitor V. Lopes, Rui C. Martins, Agostinho C. Rosa: micompr: An R Package for Multivariate Independent Comparison of Observations (2016) arXiv
  3. Patra, Rohit K.; Sen, Bodhisattva; Székely, Gábor J.: On a nonparametric notion of residual and its applications (2016)
  4. Rizzo, Maria L.; Haman, John T.: Expected distances and goodness-of-fit for the asymmetric Laplace distribution (2016)
  5. Royer-Carenzi, Manuela; Didier, Gilles: A comparison of ancestral state reconstruction methods for quantitative characters (2016)
  6. Dueck, Johannes; Edelmann, Dominic; Richards, Donald: A generalization of an integral arising in the theory of distance correlation (2015)
  7. Dueck, Johannes; Edelmann, Dominic; Gneiting, Tilmann; Richards, Donald: The affinely invariant distance correlation (2014)
  8. Lyons, Russell: Distance covariance in metric spaces (2013)
  9. Székely, Gábor J.; Rizzo, Maria L.: Energy statistics: a class of statistics based on distances (2013)
  10. Székely, Gábor J.; Rizzo, Maria L.: The distance correlation $t$-test of independence in high dimension (2013)
  11. van den Boogaart, K. Gerald; Tolosana-Delgado, Raimon: Analyzing compositional data with R (2013)
  12. Székely, Gábor J.; Rizzo, Maria L.: Brownian distance covariance (2009)
  13. Székely, Gábor J.; Rizzo, Maria L.: Rejoinder: “Brownian distance covariance” (2009)