Title: Multivariate sign tests for sphericity: Dealing with skewness and dependent observations Authors:  Gaspard Bernard - University of Luxembourg (Luxembourg) [presenting]
Abstract: The problem of testing for the sphericity of a shape parameter is considered when the sample is drawn from a distribution with elliptical directions. This setting encompasses both cases where some skewness is present and cases where the i.i.d. hypothesis does not hold anymore. In the elliptical directions setting, the existing sphericity test based on the multivariate signs of the observations is valid if the location parameter is specified when constructing the multivariate signs. In practice, the location parameter needs to be estimated, and the asymptotic validity of the test will depend on the asymptotic cost of this estimation. This asymptotic cost is studied and shown under what conditions the test based on the multivariate signs is asymptotically valid and optimal.