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. Shang, Du; Shang, Pengjian: A novel approach of dependence measure for complex signals (2022)
  2. Berrett, Thomas B.; Kontoyiannis, Ioannis; Samworth, Richard J.: Optimal rates for independence testing via (U)-statistic permutation tests (2021)
  3. Dong, Yuexiao: A brief review of linear sufficient dimension reduction through optimization (2021)
  4. Hlávka, Zdeněk; Hušková, Marie; Meintanis, Simos G.: Testing serial independence with functional data (2021)
  5. Móri, Tamás F.; Székely, Gábor J.; Rizzo, Maria L.: On energy tests of normality (2021)
  6. Peng, Liuhua; Qu, Long; Nettleton, Dan: Variable importance assessments and backward variable selection for multi-sample problems (2021)
  7. Pronzato, Luc; Zhigljavsky, Anatoly: Minimum-energy measures for singular kernels (2021)
  8. Quessy, Jean-François: A Szekely-Rizzo inequality for testing general copula homogeneity hypotheses (2021)
  9. Wick, Felix; Kerzel, Ulrich; Hahn, Martin; Wolf, Moritz; Singhal, Trapti; Stemmer, Daniel; Ernst, Jakob; Feindt, Michael: Demand forecasting of individual probability density functions with machine learning (2021)
  10. Xu, Kai; He, Daojiang: Omnibus model checks of linear assumptions through distance covariance (2021)
  11. Ebner, Bruno; Henze, Norbert: Tests for multivariate normality -- a critical review with emphasis on weighted (L^2)-statistics (2020)
  12. Edelmann, Dominic; Richards, Donald; Vogel, Daniel: The distance standard deviation (2020)
  13. Guo, Xu; Jiang, Xuejun; Zhang, Shumei; Zhu, Lixing: Pairwise distance-based heteroscedasticity test for regressions (2020)
  14. Henze, Norbert; Visagie, Jaco: Testing for normality in any dimension based on a partial differential equation involving the moment generating function (2020)
  15. Herwartz, Helmut; Maxand, Simone: Nonparametric tests for independence: a review and comparative simulation study with an application to malnutrition data in India (2020)
  16. Hlávka, Zdeněk; Hušková, Marie; Meintanis, Simos G.: Change-point methods for multivariate time-series: paired vectorial observations (2020)
  17. Kim, Ilmun; Balakrishnan, Sivaraman; Wasserman, Larry: Robust multivariate nonparametric tests via projection averaging (2020)
  18. Li, Gongkai; Tang, Minh; Charon, Nicolas; Priebe, Carey: Central limit theorems for classical multidimensional scaling (2020)
  19. Lovato, Ilenia; Pini, Alessia; Stamm, Aymeric; Vantini, Simone: Model-free two-sample test for network-valued data (2020)
  20. Opperman, Logan; Ning, Wei: Goodness-of-fit test for skew normality based on energy statistics (2020)

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