The Energy of Data and Distance Correlation

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.

能量距離是隨機向量分佈之間的統計距離，用於描述分佈的相等性。能量一詞源於牛頓的重力位能，並與統計觀察之間的位能概念有一個優雅的關聯。能量統計是度量空間中統計觀察之間距離的函數。作者希望這本書能引起大多數統計學家的興趣，他們迄今尚未探索E統計學，並希望能夠使用R應用這些新方法。《數據能量與距離相關性》旨在為尋找專門材料的教師和學生提供能量統計的概述，但也可作為各種課程和領域的補充，如蒙特卡洛方法、U統計或V統計、多變量相依性測量、適配度檢驗、非參數方法和基於距離的方法。

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

is Professor in the Department of Mathematics and Statistics at Bowling Green State University in Bowling Green, Ohio, where she teaches statistics, actuarial science, computational statistics, statistical programming and data science. Prior to joining the faculty at BGSU in 2006, she was a faculty member of the Department of Mathematics at Ohio University in Athens, Ohio. Her main research area is energy statistics and distance correlation. She is the software developer and maintainer of the energy package for R, and author of textbooks on statistical computing: "Statistical Computing with R" 1st and 2nd editions, "R by Example" (2nd edition in progress) with Jim Albert, and a forthcoming textbook on data science. Dr. Rizzo has eight PhD students and one current student, almost all with dissertations on energy statistics. Outside of work she enjoys spending time with her family including her husband, daughters, grandchildren and a large extended family.

Gábor J. Székely於1970年在匈牙利布達佩斯的Eötvös Loránd大學（ELTE）獲得碩士學位，並於1971年獲得博士學位。他於1970年加入了ELTE的概率論系。1989年，他成為布達佩斯科技學院（布達佩斯科技大學）隨機過程系的創立主席。1995年，Székely移居美國。在此之前，他於1990-91年擔任俄亥俄州鮑靈格林州立大學的第一位傑出Lukacs教授。Székely曾擔任多個訪問職位，例如1976年在阿姆斯特丹大學和1989年在耶魯大學。1985年至1995年期間，他是布達佩斯數學學期的第一位匈牙利籍主任。2006年至2022年，直到退休前，他擔任美國國家科學基金會統計學項目主任。Székely發表了近250篇論文，包括幾本以多種語言出版的書籍。1988年，他與Imre Z. Ruzsa共同獲得劍橋大學頒發的Rollo Davidson獎，以表彰他們在代數概率論方面的工作。2010年，Székely因其在統計學中物理概念（如能量統計和距離相關性）方面的開創性工作，成為數學統計學會的當選會士。Székely曾應邀在多個聯合統計會議上發表演講，並組織了關於能量統計和距離相關性的特邀會議。Székely有兩個孩子，Szilvia和Tamás，以及六個孫子女：Elisa、Anna、Michaël和Lea、Eszter、Avi，他們居住在比利時的布魯塞爾和瑞士的巴塞爾。Székely和他的妻子Judit居住在維吉尼亞州麥克林和匈牙利的布達佩斯。

Maria L. Rizzo是俄亥俄州鮑靈格林市Bowling Green State大學數學和統計學系的教授，教授統計學、精算學、計算統計學、統計程式設計和數據科學。在2006年加入BGSU教職之前，她曾是俄亥俄州阿森斯市俄亥俄大學數學系的教職成員。她的主要研究領域是能量統計和距離相關性。她是R語言能量統計套件的軟體開發者和維護者，並撰寫了有關統計計算的教科書：《使用R進行統計計算》第1版和第2版，《R範例》（第2版正在進行中）與Jim Albert合著，以及一本即將出版的數據科學教科書。Rizzo博士指導了八位博士生和一位在讀學生，幾乎所有人的論文都是關於能量統計。在工作之外，她喜歡與家人共度時光，包括丈夫、女兒、孫子和一大群親戚。