Multivariate Statistical Methods - György Terdik

Multivariate Statistical Methods

Going Beyond the Linear

(Autor)

Buch | Softcover
XIV, 418 Seiten
2022 | 1st ed. 2021
Springer International Publishing (Verlag)
978-3-030-81394-9 (ISBN)
117,69 inkl. MwSt

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.


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.

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.

"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)

“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)

Erscheinungsdatum
Reihe/Serie Frontiers in Probability and the Statistical Sciences
Zusatzinfo XIV, 418 p.
Verlagsort Cham
Sprache englisch
Maße 155 x 235 mm
Gewicht 658 g
Themenwelt Mathematik / Informatik Mathematik Computerprogramme / Computeralgebra
Mathematik / Informatik Mathematik Statistik
Mathematik / Informatik Mathematik Wahrscheinlichkeit / Kombinatorik
Schlagworte Cumulants • Fourier transform • Hermite Polynomials • kurtosis • Multivariate distributions • Multivariate skewness and kurtosis • Multivariate Statistical Methods • Skewness
ISBN-10 3-030-81394-0 / 3030813940
ISBN-13 978-3-030-81394-9 / 9783030813949
Zustand Neuware
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