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. Bilodeau, Martin; Nangue, Aurélien Guetsop: Tests of mutual or serial independence of random vectors with applications (2017)
  2. Fan, Yanan; de Micheaux, Pierre Lafaye; Penev, Spiridon; Salopek, Donna: Multivariate nonparametric test of independence (2017)
  3. Saha, Enakshi; Sarkar, Soham; Ghosh, Anil K.: Some high-dimensional one-sample tests based on functions of interpoint distances (2017)
  4. van den Boogaart, K. Gerald; Mueller, Ute; Tolosana-Delgado, Raimon: An affine equivariant multivariate normal score transform for compositional data (2017)
  5. Woodrow Burchett and Amanda Ellis and Solomon Harrar and Arne Bathke: Nonparametric Inference for Multivariate Data: The R Package npmv (2017)
  6. Biau, Gérard; Bleakley, Kevin; Mason, David M.: Long signal change-point detection (2016)
  7. Hernández-Lobato, Daniel; Morales-Mombiela, Pablo; Lopez-Paz, David; Suárez, Alberto: Non-linear causal inference using Gaussianity measures (2016)
  8. Nandy, Preetam; Weihs, Luca; Drton, Mathias: Large-sample theory for the Bergsma-Dassios sign covariance (2016)
  9. 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
  10. Patra, Rohit K.; Sen, Bodhisattva; Székely, Gábor J.: On a nonparametric notion of residual and its applications (2016)
  11. Rizzo, Maria L.; Haman, John T.: Expected distances and goodness-of-fit for the asymmetric Laplace distribution (2016)
  12. Royer-Carenzi, Manuela; Didier, Gilles: A comparison of ancestral state reconstruction methods for quantitative characters (2016)
  13. Székely, Gábor J.; Rizzo, Maria L.: Partial distance correlation (2016)
  14. Dueck, Johannes; Edelmann, Dominic; Richards, Donald: A generalization of an integral arising in the theory of distance correlation (2015)
  15. Dueck, Johannes; Edelmann, Dominic; Gneiting, Tilmann; Richards, Donald: The affinely invariant distance correlation (2014)
  16. Székely, Gábor J.; Rizzo, Maria L.: Partial distance correlation with methods for dissimilarities (2014)
  17. Lyons, Russell: Distance covariance in metric spaces (2013)
  18. Rocha, Conceição; Mendonça, Teresa; Silva, Maria Eduarda: Modelling neuromuscular blockade: a stochastic approach based on clinical data (2013)
  19. Székely, Gábor J.; Rizzo, Maria L.: The distance correlation $t$-test of independence in high dimension (2013)
  20. Székely, Gábor J.; Rizzo, Maria L.: Energy statistics: a class of statistics based on distances (2013)

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