On Generalized Wishart Distributions - II: Sphericity Test

Francisco J. Caro-Lopera; Graciela González-Farías; N. Balakrishnan

doi:10.1007/s13171-013-0049-5

On Generalized Wishart Distributions - II: Sphericity Test

Francisco J. Caro-Lopera, Graciela González-Farías, N. Balakrishnan

Grupo de Investigación en Materiales Nanoestructurados y Biomodelación

Resultado de la investigación: Contribución a una revista › Artículo › revisión exhaustiva

Resumen

© 2014, Indian Statistical Institute. In this second part of the paper, we make use of the distribution of the trace of a generalized Wishart matrix based on elliptical models to derive the moments of statistic V used for testing sphericity for a general elliptical model. From the general expressions, we derive specific expressions for the special case of the Kotz family, which includes the Gaussian subfamily. Finally, to illustrate the usefulness of the approach, the exact distribution of the statistic V is derived in terms of the G-function by using Mellin transform and complex integration techniques.

Idioma original	Inglés estadounidense
Páginas (desde-hasta)	195-218
Número de páginas	24
Publicación	Sankhya A
DOI	https://doi.org/10.1007/s13171-013-0049-5
Estado	Publicada - 1 ago 2014

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N2 - © 2014, Indian Statistical Institute. In this second part of the paper, we make use of the distribution of the trace of a generalized Wishart matrix based on elliptical models to derive the moments of statistic V used for testing sphericity for a general elliptical model. From the general expressions, we derive specific expressions for the special case of the Kotz family, which includes the Gaussian subfamily. Finally, to illustrate the usefulness of the approach, the exact distribution of the statistic V is derived in terms of the G-function by using Mellin transform and complex integration techniques.

AB - © 2014, Indian Statistical Institute. In this second part of the paper, we make use of the distribution of the trace of a generalized Wishart matrix based on elliptical models to derive the moments of statistic V used for testing sphericity for a general elliptical model. From the general expressions, we derive specific expressions for the special case of the Kotz family, which includes the Gaussian subfamily. Finally, to illustrate the usefulness of the approach, the exact distribution of the statistic V is derived in terms of the G-function by using Mellin transform and complex integration techniques.

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