Multivariate Statistical Methods: Going Beyond the Linear (Frontiers in Probability and the Statistical Sciences) - Hardcover

Terdik, György

Hardcover

ISBN 10: 3030813916 ISBN 13: 9783030813918

Publisher: Springer, 2021

Synopsis

This book presents a general method for deriving higher-order statistics of multivariate distributions with simple algorithms that allow for actual calculations. Multivariate nonlinear statistical models require the study of higher-order moments and cumulants. The main tool used for the definitions is the tensor derivative, leading to several useful expressions concerning Hermite polynomials, moments, cumulants, skewness, and kurtosis. A general test of multivariate skewness and kurtosis is obtained from this treatment. Exercises are provided for each chapter to help the readers understand the methods. Lastly, the book includes a comprehensive list of references, equipping readers to explore further on their own.

About this title

About the Author

György Terdik received his PhD in 1982 at the Department of Probability Theory, State University of Leningrad, USSR. He has been a full-time professor at the Faculty of Informatics, University of Debrecen, Hungary since 2008. He has spent 10 semesters visiting different universities in the US including UC Berkeley and UC Santa Barbara, and the Case Western Reserve University, among others.

His research interests include multivariate nonlinear statistics, time series analysis, modelling high speed communication networks, bilinear and multi-fractal models, directional statistics, and spherical processes, spatial dependence and interaction between space and time.

From the Back Cover

This book presents a general method for deriving higher-order statistics of multivariate distributions with simple algorithms that allow for actual calculations. Multivariate nonlinear statistical models require the study of higher-order moments and cumulants. The main tool used for the definitions is the tensor derivative, leading to several useful expressions concerning Hermite polynomials, moments, cumulants, skewness, and kurtosis. A general test of multivariate skewness and kurtosis is obtained from this treatment. Exercises are provided for each chapter to help the readers understand the methods. Lastly, the book includes a comprehensive list of references, equipping readers to explore further on their own.

Edition details

• Publisher: Springer
• Publication date: 2021
• Language: English
• ISBN 10: 3030813916
• ISBN 13: 9783030813918
• Binding: Hardcover
• Edition number: 1
• Number of pages: 432