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B1152
Title: Shape depth Authors:  Germain Van Bever - Universite de Namur (Belgium) [presenting]
Davy Paindaveine - Universite libre de Bruxelles (Belgium)
Abstract: In many problems from multivariate analysis (principal component analysis, testing for sphericity, etc.), the parameter of interest is not the scatter matrix but the so-called shape matrix, that is, a normalised version of the corresponding dispersion matrices. We propose, under elliptical assumptions, a depth concept for shape. If shape matrices are normalised to have determinant one, our shape depth results from a previous parametric depth construction. For other normalisations, however, defining a proper shape depth requires a semiparametric extension of this construction, which is likely to have applications in other contexts. We show that the proposed shape depth does not depend on the normalisation adopted and is affine-invariant. We also establish consistency, in the sense that shape depth is maximised at the true shape value. Finally, we consider depth-based tests for shape, and investigate their finite-sample performances through simulations.