ANOVA; Directional statistics; Local asymptotic normality; Pseudo-FvML tests; Rank-based inference; Asymptotic relative efficiency; Directional data; Finite sample behavior; Invariance principle; Local asymptotic normalities; Symmetric distributions; Statistics and Probability
Abstract :
[en] In this paper, we tackle the ANOVA problem for directional data. We apply the invariance principle to construct locally and asymptotically most stringent rank-based tests. Our semi-parametric tests improve on the optimal parametric tests by being valid under the whole class of rotationally symmetric distributions. Moreover, they keep the optimality property of the latter under a given m-tuple of rotationally symmetric distributions. Asymptotic relative efficiencies are calculated and the finite-sample behavior of the proposed tests is investigated by means of a Monte Carlo simulation. We conclude by applying our findings to a real-data example involving geological data.
Disciplines :
Mathematics
Author, co-author :
LEY, Christophe ; University of Luxembourg > Faculty of Science, Technology and Medicine (FSTM) > Department of Mathematics (DMATH) ; Département de Mathématique and ECARES, Université libre de Bruxelles (ULB), Brussels, Belgium
Swan, Yvik; Département de Mathématique, Université de Liège, Liège, Belgium
Verdebout, Thomas; Département de Mathématique and ECARES, Université libre de Bruxelles (ULB), Brussels, Belgium
External co-authors :
yes
Language :
English
Title :
Efficient ANOVA for directional data
Publication date :
February 2017
Journal title :
Annals of the Institute of Statistical Mathematics
We would like to thank the Associate Editor and two anonymous referees for helpful comments that have led to a clear improvement of our paper. The research of Christophe Ley is supported by a Mandat de Chargé de Recherche from the Fonds National de la Recherche Scientifique, Communauté française de Belgique. Yvik Swan gratefully acknowledges support from the IAP Research Network P7/06 of the Belgian State (Belgian Science Policy).
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