A General Method for Constructing Pseudo-Gaussian Tests

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  • Hallin Marc
    E.C.A.R.E.S., Institut de Recherche en Statistique, and Département de Mathématique, Université Libre de Bruxelles
  • Paindaveine Davy
    E.C.A.R.E.S., Institut de Recherche en Statistique, and Département de Mathématique, Université Libre de Bruxelles

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Abstract

A general method for constructing pseudo-Gaussian tests—reducing to traditional Gaussian tests under Gaussian densities but remaining valid under non-Gaussian ones—is proposed. This method provides a solution to several open problems in classical multivariate analysis. One of them is the test of the homogeneity of covariance matrices, an assumption that plays a crucial role in multivariate analysis of variance, under elliptical, and possibly heterokurtic densities with finite fourth-order moments.

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