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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