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. Dong, Yuexiao: A brief review of linear sufficient dimension reduction through optimization (2021)
  2. Móri, Tamás F.; Székely, Gábor J.; Rizzo, Maria L.: On energy tests of normality (2021)
  3. Pronzato, Luc; Zhigljavsky, Anatoly: Minimum-energy measures for singular kernels (2021)
  4. Edelmann, Dominic; Richards, Donald; Vogel, Daniel: The distance standard deviation (2020)
  5. Guo, Xu; Jiang, Xuejun; Zhang, Shumei; Zhu, Lixing: Pairwise distance-based heteroscedasticity test for regressions (2020)
  6. Henze, Norbert; Visagie, Jaco: Testing for normality in any dimension based on a partial differential equation involving the moment generating function (2020)
  7. Herwartz, Helmut; Maxand, Simone: Nonparametric tests for independence: a review and comparative simulation study with an application to malnutrition data in India (2020)
  8. Hlávka, Zdeněk; Hušková, Marie; Meintanis, Simos G.: Change-point methods for multivariate time-series: paired vectorial observations (2020)
  9. Kim, Ilmun; Balakrishnan, Sivaraman; Wasserman, Larry: Robust multivariate nonparametric tests via projection averaging (2020)
  10. Li, Gongkai; Tang, Minh; Charon, Nicolas; Priebe, Carey: Central limit theorems for classical multidimensional scaling (2020)
  11. Lovato, Ilenia; Pini, Alessia; Stamm, Aymeric; Vantini, Simone: Model-free two-sample test for network-valued data (2020)
  12. Opperman, Logan; Ning, Wei: Goodness-of-fit test for skew normality based on energy statistics (2020)
  13. Pronzato, Luc; Zhigljavsky, Anatoly: Bayesian quadrature, energy minimization, and space-filling design (2020)
  14. Romano, Yaniv; Sesia, Matteo; Candès, Emmanuel: Deep knockoffs (2020)
  15. Sang, Yongli; Dang, Xin: Empirical likelihood test for diagonal symmetry (2020)
  16. Sarkar, Soham; Biswas, Rahul; Ghosh, Anil K.: On some graph-based two-sample tests for high dimension, low sample size data (2020)
  17. Shen, Cencheng; Priebe, Carey E.; Vogelstein, Joshua T.: From distance correlation to multiscale graph correlation (2020)
  18. Chakraborty, Shubhadeep; Zhang, Xianyang: Distance metrics for measuring joint dependence with application to causal inference (2019)
  19. Chen, Feifei; Meintanis, Simos G.; Zhu, Lixing: On some characterizations and multidimensional criteria for testing homogeneity, symmetry and independence (2019)
  20. Cui, Hengjian; Zhong, Wei: A distribution-free test of independence based on mean variance index (2019)

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