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. Betsch, Steffen; Ebner, Bruno; Nestmann, Franz: Characterizations of non-normalized discrete probability distributions and their application in statistics (2022)
  2. Chen, Bo; Wang, Hai-meng: High-dimensional tests for mean vector: approaches without estimating the mean vector directly (2022)
  3. Ghosal, Promit; Sen, Bodhisattva: Multivariate ranks and quantiles using optimal transport: consistency, rates and nonparametric testing (2022)
  4. Guo, Lingzhe; Modarres, Reza: Two multivariate online change detection models (2022)
  5. Herwartz, Helmut: Modelling interaction patterns in a predator-prey system of two freshwater organisms in discrete time: an identified structural VAR approach (2022)
  6. Hlávka, Zdeněk; Hlubinka, Daniel; Koňasová, Kateřina: Functional ANOVA based on empirical characteristic functionals (2022)
  7. James, Nick; Menzies, Max; Bondell, Howard: Comparing the dynamics of COVID-19 infection and mortality in the United States, India, and Brazil (2022)
  8. Jiang, Hangjin; Zhao, Xingqiu; Ma, Ronald C. W.; Fan, Xiaodan: Consistent screening procedures in high-dimensional binary classification (2022)
  9. Liu, Jicai; Si, Yuefeng; Xu, Wenchao; Zhang, Riquan: A new nonparametric extension of ANOVA via projection mean variance measure (2022)
  10. Paul, Biplab; De, Shyamal K.; Ghosh, Anil K.: Some clustering-based exact distribution-free (k)-sample tests applicable to high dimension, low sample size data (2022)
  11. Shang, Du; Shang, Pengjian: A novel approach of dependence measure for complex signals (2022)
  12. Al-Labadi, Luai; Fazeli Asl, Forough; Saberi, Zahra: A necessary Bayesian nonparametric test for assessing multivariate normality (2021)
  13. Berrett, Thomas B.; Kontoyiannis, Ioannis; Samworth, Richard J.: Optimal rates for independence testing via (U)-statistic permutation tests (2021)
  14. Dong, Yuexiao: A brief review of linear sufficient dimension reduction through optimization (2021)
  15. Hlávka, Zdeněk; Hušková, Marie; Meintanis, Simos G.: Testing serial independence with functional data (2021)
  16. Móri, Tamás F.; Székely, Gábor J.; Rizzo, Maria L.: On energy tests of normality (2021)
  17. Peng, Liuhua; Qu, Long; Nettleton, Dan: Variable importance assessments and backward variable selection for multi-sample problems (2021)
  18. Pronzato, Luc; Zhigljavsky, Anatoly: Minimum-energy measures for singular kernels (2021)
  19. Quessy, Jean-François: A Szekely-Rizzo inequality for testing general copula homogeneity hypotheses (2021)
  20. 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)

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