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.
Arvustused
The book under review is a very well-written monograph, which gives an up-to-date, self-contained, and thorough analysis of the cumulants and related statistical measures like the skewness and kurtosis for non-Gaussian multivariate distributions. From my point of view, the author has written an interesting book, which could be a reference book for researchers interested in multivariate analysis as well as text for advanced graduate-level courses. (Apostolos Batsidis, zbMATH 1512.62005, 2023)
Some Introductory Algebra.- Tensor derivative of vector functions.-
T-Moments and T-Cumulants.- Gaussian systems, T-Hermite polynomials, Moments
and Cumulants.- Multivariate Skew Distributions.- Multivariate skewness and
kurtosis.
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.
