Energy statistics are functions of distances between statistical observations in metric spaces. The authors hope this book will spark the interest of most statisticians who so far have not explored E-statistics and would like to apply these new methods using R.
Gábor J. Székely graduated from Eötvös Loránd University, Budapest, Hungary (ELTE) with MS in 1970, and Ph. D. in 1971. He joined the Department of Probability Theory of ELTE in 1970. In 1989 he became the funding chair of the Department of Stochastics of the Budapest Institute of Technology (Technical University of Budapest). In 1995 Székely moved to the US. Before that, in 1990-91 he was the first distinguished Lukacs Professor at Bowling Green State University, Ohio. Székely had several visiting positions, e.g., at the University of Amsterdam in 1976 and at Yale University in 1989. Between 1985 and 1995 he was the first Hungarian director of Budapest Semesters in Mathematics. Between 2006 and 2022, until his retirement, he was program director of statistics of the National Science Foundation (USA). Székely has almost 250 publications, including six books in several languages. In 1988 he received the Rollo Davidson Prize from Cambridge University, jointly with Imre Z. Ruzsa for their work on algebraic probability theory. In 2010 Székely became an elected fellow of the Institute of Mathematical Statistics for his seminal work on physics concepts in statistics like energy statistics and distance correlation. Székely was invited speaker at several Joint Statistics Meetings and also organizer of invited sessions on energy statistics and distance correlation. Székely has two children, Szilvia and Tamás, and six grandchildren: Elisa, Anna, Michaël and Lea, Eszter, Avi who live in Brussels, Belgium and Basel, Switzerland. Székely and his wife, Judit, live in McLean, Virginia and Budapest, Hungary.
Maria L. Rizzo
Part 1: The Energy of Data 1. Introduction 2. Preliminaries 3. Energy Distance 4. Introduction to Energy Inference 5. Goodness-of-Fit 6. Testing Multivariate Normality 7. Eigenvalues for One-Sample E-Statistics 8. Generalized Goodness-of-Fit 9. Multi-sample Energy Statistics 10. Energy in Metric Spaces and Other Distances Part 2: Distance Correlation and Dependence 11. On Correlation and Other Measures of Association 12. Distance Correlation 13. Testing Independence 14. Applications and Extensions 15. Brownian Distance Covariance 16. U-statistics and Unbiased dCov2 17. Partial Distance Correlation 18. The Numerical Value of dCor 19. The dCor t-test of Independence in High Dimension 20. Computational Algorithms 21. Time Series and Distance Correlation 22. Axioms of Dependence Measures 23. Earth Mover's Correlation 24. Appendix A: Historical Background 25. Appendix B: Prehistory