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Efficient ANOVA for directional data

Christophe Ley (), Yvik Swan () and Thomas Verdebout ()
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Christophe Ley: Université libre de Bruxelles (ULB)
Yvik Swan: Université de Liège
Thomas Verdebout: Université libre de Bruxelles (ULB)

Annals of the Institute of Statistical Mathematics, 2017, vol. 69, issue 1, 39-62

Abstract: Abstract 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.

Keywords: Directional statistics; Local asymptotic normality; Pseudo-FvML tests; Rank-based inference; ANOVA (search for similar items in EconPapers)
Date: 2017
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