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Multivariate Statistical Methods

Going Beyond the Linear

  • Book
  • © 2021

Overview

Authors:
  1. György Terdik

    1. Faculty of Informatics, Dept. of IT, University of Debrecen, Debrecen, Hungary

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  • 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

Part of the book series: Frontiers in Probability and the Statistical Sciences (FROPROSTAS)

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Table of contents (6 chapters)

  1. Front Matter

    Pages i-xiv
    Download chapter PDF

  2. Some Introductory Algebra

    • György Terdik
    Pages 1-59

  3. The Tensor Derivative of Vector Functions

    • György Terdik
    Pages 61-106

  4. T-Moments and T-Cumulants

    • György Terdik
    Pages 107-181

  5. Gaussian Systems, T-Hermite Polynomials, Moments, and Cumulants

    • György Terdik
    Pages 183-239

  6. Multivariate Skew Distributions

    • György Terdik
    Pages 241-311

  7. Multivariate Skewness and Kurtosis

    • György Terdik
    Pages 313-349

  8. Back Matter

    Pages 351-418
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Keywords

About this book

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.


Reviews

“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)

Authors and Affiliations

  • Faculty of Informatics, Dept. of IT, University of Debrecen, Debrecen, Hungary

    György Terdik

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.


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