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B0255
Title: Optimal tests for elliptical symmetry against skew-elliptical alternatives Authors:  Christophe Ley - University of Luxembourg (Luxembourg) [presenting]
Marc Hallin - Universite Libre de Bruxelles (Belgium)
Laetitia Gelbgras - Universite libre de Bruxelles (Belgium)
Abstract: The majority of statistical procedures involving multivariate data assumes elliptical symmetry of the data at hand. This assumption, however, is often violated, especially in finance. A very popular alternative are the skew-elliptical distributions, obtained by multiplying elliptically symmetric densities with a skewing function. We shall show how to build tests for elliptical symmetry that are designed to be optimal against skew-elliptical distributions. Starting from optimal parametric tests (in the spirit of score tests), we shall render them semi-parametric and hence valid in the entire class of elliptical distributions, yet they shall inherit optimality properties from their parametric antecedents. One particular aspect of our tests is that they will not require the typical constraint of finite high-order moment assumptions. This is particularly useful when dealing with financial data, which are often heavy-tailed. We shall illustrate the benefits of these new tests by analyzing data from major stock markets.