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Multivariate Statistical Methods: Going Beyond the Linear de György Terdik

Multivariate Statistical Methods: Going Beyond the Linear: Frontiers in Probability and the Statistical Sciences

Autor György Terdik
en Limba Engleză Paperback – 28 oct 2022
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.

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Specificații

ISBN-13: 9783030813949
ISBN-10: 3030813940
Pagini: 418
Ilustrații: XIV, 418 p.
Dimensiuni: 155 x 235 mm
Greutate: 0.6 kg
Ediția:1st ed. 2021
Editura: Springer International Publishing
Colecția Springer
Seria Frontiers in Probability and the Statistical Sciences

Locul publicării:Cham, Switzerland

Cuprins

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.

Recenzii

“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)

Notă biografică

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.


Textul de pe ultima copertă

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.


Caracteristici

Presents a general method for deriving higher order statistics of multivariate distributions Discusses multivariate skewness and kurtosis; provides ready-to-use expressions for estimating and testing Provides exercises for each chapter and a list of references