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On Generalized Wishart Distributions - II: Sphericity Test

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Abstract

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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Authors and Affiliations

  1. Departamento de Ciencias Básicas, Universidad de Medellín, Medellín, Colombia

    Francisco J. Caro-Lopera

  2. Centro de Investigación en Matemáticas, Monterrey, México

    Graciela González-Farías

  3. Department of Mathematics and Statistics, McMaster University Hamilton, Ontario, Canada

    N. Balakrishnan

  4. Department of Statistics, King AbdulAziz University, Jeddah, Saudi Arabia

    N. Balakrishnan

Authors
  1. Francisco J. Caro-Lopera
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  2. Graciela González-Farías
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  3. N. Balakrishnan
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Correspondence to Graciela González-Farías.

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Caro-Lopera, F.J., González-Farías, G. & Balakrishnan, N. On Generalized Wishart Distributions - II: Sphericity Test. Sankhya A 76, 195–218 (2014). https://doi.org/10.1007/s13171-013-0049-5

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  • DOI: https://doi.org/10.1007/s13171-013-0049-5

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