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. Lovato, Ilenia; Pini, Alessia; Stamm, Aymeric; Vantini, Simone: Model-free two-sample test for network-valued data (2020)
  2. Sang, Yongli; Dang, Xin: Empirical likelihood test for diagonal symmetry (2020)
  3. Sarkar, Soham; Biswas, Rahul; Ghosh, Anil K.: On some graph-based two-sample tests for high dimension, low sample size data (2020)
  4. Chakraborty, Shubhadeep; Zhang, Xianyang: Distance metrics for measuring joint dependence with application to causal inference (2019)
  5. Chen, Feifei; Meintanis, Simos G.; Zhu, Lixing: On some characterizations and multidimensional criteria for testing homogeneity, symmetry and independence (2019)
  6. Cui, Hengjian; Zhong, Wei: A distribution-free test of independence based on mean variance index (2019)
  7. Curry, Jamye; Dang, Xin; Sang, Hailin: A rank-based Cramér-von-Mises-type test for two samples (2019)
  8. Dette, Holger; Pepelyshev, Andrey; Zhigljavsky, Anatoly: The BLUE in continuous-time regression models with correlated errors (2019)
  9. Febrero-Bande, Manuel; González-Manteiga, Wenceslao; Oviedo de la Fuente, Manuel: Variable selection in functional additive regression models (2019)
  10. Jiang, Qing; Hušková, Marie; Meintanis, Simos G.; Zhu, Lixing: Asymptotics, finite-sample comparisons and applications for two-sample tests with functional data (2019)
  11. Lee, Sangyeol; Meintanis, Simos G.; Jo, Minyoung: Inferential procedures based on the integrated empirical characteristic function (2019)
  12. Pronzato, Luc; Wynn, Henry P.; Zhigljavsky, Anatoly: Bregman divergences based on optimal design criteria and simplicial measures of dispersion (2019)
  13. Talebi, Hassan; Mueller, Ute; Tolosana-Delgado, Raimon; van den Boogaart, K. Gerald: Geostatistical simulation of geochemical compositions in the presence of multiple geological units: application to mineral resource evaluation (2019)
  14. Verdinelli, Isabella; Wasserman, Larry: Hybrid Wasserstein distance and fast distribution clustering (2019)
  15. Zhang, Kai: BET on independence (2019)
  16. Allison, James S.; Hušková, M.; Meintanis, Simos G.: Testing the adequacy of semiparametric transformation models (2018)
  17. Athreya, Avanti; Fishkind, Donniell E.; Tang, Minh; Priebe, Carey E.; Park, Youngser; Vogelstein, Joshua T.; Levin, Keith; Lyzinski, Vince; Qin, Yichen; Sussman, Daniel L.: Statistical inference on random dot product graphs: a survey (2018)
  18. Dai, Xinjie; Niu, Cuizhen; Guo, Xu: Testing for central symmetry and inference of the unknown center (2018)
  19. González-Estrada, E.; Villaseñor, J. A.: An R package for testing goodness of fit: goft (2018)
  20. Jin, Ze; Matteson, David S.: Generalizing distance covariance to measure and test multivariate mutual dependence via complete and incomplete V-statistics (2018)

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