Circular statistics; Le Cam asymptotic theory; Semi-parametric tests; Sine-skewed distributions; Statistics and Probability; Statistics, Probability and Uncertainty
Abstract :
[en] Symmetry is one of the most fundamental of dividing hypotheses, its rejection, or not, heavily influencing subsequent modeling strategies. In this paper, the authors construct tests for circular reflective symmetry about an unknown central direction that are asymptotically valid within a semi-parametric class of distributions and maintain certain parametric local and asymptotic optimality properties. The asymptotic distributions of the test statistics under the null hypothesis and under local alternatives are established, and a pre-existing omnibus test is identified as a special case of the proposed construction. The finite-sample properties of the semi-parametric tests are compared with those of other testing approaches in a simulation experiment, and recommendations made regarding testing for reflective symmetry in practice. Analyses of data on the directions of cracks in hip replacements illustrate the proposed methodology.
Ameijeiras-Alonso, Jose ; Statistics Section, Department of Mathematics, KU Leuven, Leuven, Belgium
LEY, Christophe ; University of Luxembourg > Faculty of Science, Technology and Medicine (FSTM) > Department of Mathematics (DMATH) ; Department of Applied Mathematics, Computer Science and Statistics, Ghent University, Ghent, Belgium
Pewsey, Arthur; Department of Mathematics, University of Extremadura, Cáceres, Spain
Verdebout, Thomas; Mathematics Department, Université Libre de Bruxelles, Brussels, Belgium
External co-authors :
yes
Language :
English
Title :
On optimal tests for circular reflective symmetry about an unknown central direction
Publication date :
August 2021
Journal title :
Statistical Papers
ISSN :
0932-5026
Publisher :
Springer Science and Business Media Deutschland GmbH
Agencia Estatal de Investigación Junta de Extremadura Flemish Science Foundation KU Leuven Ministerio de Economía y Competitividad Agencia Estatal de Investigación Junta de Extremadura Fonds National pour la Recherche Scientifique
Funding text :
We would like to thank two anonymous referees for their insightful and helpful comments on a previous draft of the paper.
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