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. 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. The Energy of Data and Distance Correlation is intended for teachers and students looking for dedicated material on energy statistics, but can serve as a supplement to a wide range of courses and areas, such as Monte Carlo methods, U-statistics or V-statistics, measures of multivariate dependence, goodness-of-fit tests, nonparametric methods and distance based methods.
•E-statistics provides powerful methods to deal with problems in multivariate inference and analysis.
•Methods are implemented in R, and readers can immediately apply them using the freely available energy package for R.
•The proposed book will provide an overview of the existing state-of-the-art in development of energy statistics and an overview of applications.
•Background and literature review is valuable for anyone considering further research or application in energy statistics.
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
"Many dozens of theorems are proved, various R codes with numerical examples are provided, and multiple exercises are given in each chapter... The book and corresponding software can be useful for instructors and students in advanced statistical courses, and for researchers and practitioners in data analysis."
Stan Lipovetsky, Ipsos, Technometrics, 22nd August 2023.