Multivariate statistical methods

• Verfasst von: Terdik, György [VerfasserIn]
• Titel: Multivariate statistical methods
• Titelzusatz: going beyond the linear : vector-moments and vector-cumulants, nonlinear statistics of normal multivariates, testing skewness and kurtosis
• Verf.angabe: Terdik, György
• Verlagsort: Cham ; Springer
• E-Jahr: 2021
• Jahr: [2021]
• Umfang: xiv, 418 Seiten
• Gesamttitel/Reihe: Frontiers in probability and the statistical sciences
• Fussnoten: Includes bibliographical references and index
• ISBN: 978-3-030-81391-8
• Schlagwörter: (s)Statistik
• Sprache: eng
• Bibliogr. Hinweis: Erscheint auch als : Online-Ausgabe: Terdik, György: Multivariate Statistical Methods. - Cham : Springer, 2021. - 1 Online-Ressource (XIV, 418 p.)
• RVK-Notation: SK 830
• K10plus-PPN: 1765980194

Abstract

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.

Abstract

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.