Tests of Concentration for Low-Dimensional and High-Dimensional Directional Data

Christine Cutting, Davy Paindaveine and Thomas Verdebout

Working Papers ECARES from ULB -- Universite Libre de Bruxelles

Abstract: We consider asymptotic inference for the concentration of directional data. More precisely, wepropose tests for concentration (i) in the low-dimensional case where the sample size n goes to infinity andthe dimension p remains fixed, and (ii) in the high-dimensional case where both n and p become arbitrarilylarge. To the best of our knowledge, the tests we provide are the first procedures for concentration thatare valid in the (n; p)-asymptotic framework. Throughout, we consider parametric FvML tests, that areguaranteed to meet asymptotically the nominal level constraint under FvML distributions only, as well as“pseudo-FvML” versions of such tests, that are validity-robust within the class of rotationally symmetricdistributions.We conduct a Monte-Carlo study to check our asymptotic results and to investigate the finitesamplebehavior of the proposed tests.

Pages: 16 p.
Date: 2015-02
New Economics Papers: this item is included in nep-ecm and nep-mfd
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