The Energy of Data and Distance Correlation

ISBN-13: 9781482242744 / Angielski / Twarda / 2023 / 452 str.

Maria L. Rizzo

Opis

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.

Recenzje

"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.

Spis treści

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