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Efficient ANOVA for directional data

Christophe Ley UGent, Yvik Swan and Thomas Verdebout (2017) ANNALS OF THE INSTITUTE OF STATISTICAL MATHEMATICS. 69(1). p.39-62
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.
Please use this url to cite or link to this publication:
author
organization
year
type
journalArticle (original)
publication status
published
subject
keyword
Directional statistics, Local asymptotic normality, Pseudo-FvML tests, Rank-based inference, ANOVA, COMMON PRINCIPAL COMPONENTS, MEAN DIRECTIONS, R-ESTIMATION, RANK-TESTS, FOLD TEST, DISTRIBUTIONS, PALEOMAGNETISM, CIRCLE, SPHERE, FAMILY
journal title
ANNALS OF THE INSTITUTE OF STATISTICAL MATHEMATICS
Ann. Inst. Stat. Math.
volume
69
issue
1
pages
39 - 62
Web of Science type
Article
Web of Science id
000391449500002
ISSN
0020-3157
DOI
10.1007/s10463-015-0533-x
language
English
UGent publication?
no
classification
A1
id
7066021
handle
http://hdl.handle.net/1854/LU-7066021
date created
2016-02-02 09:19:21
date last changed
2017-04-26 11:08:25
@article{7066021,
  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.},
  author       = {Ley, Christophe and Swan, Yvik and Verdebout, Thomas},
  issn         = {0020-3157},
  journal      = {ANNALS OF THE INSTITUTE OF STATISTICAL MATHEMATICS},
  keyword      = {Directional statistics,Local asymptotic normality,Pseudo-FvML tests,Rank-based inference,ANOVA,COMMON PRINCIPAL COMPONENTS,MEAN DIRECTIONS,R-ESTIMATION,RANK-TESTS,FOLD TEST,DISTRIBUTIONS,PALEOMAGNETISM,CIRCLE,SPHERE,FAMILY},
  language     = {eng},
  number       = {1},
  pages        = {39--62},
  title        = {Efficient ANOVA for directional data},
  url          = {http://dx.doi.org/10.1007/s10463-015-0533-x},
  volume       = {69},
  year         = {2017},
}

Chicago
Ley, Christophe, Yvik Swan, and Thomas Verdebout. 2017. “Efficient ANOVA for Directional Data.” Annals of the Institute of Statistical Mathematics 69 (1): 39–62.
APA
Ley, C., Swan, Y., & Verdebout, T. (2017). Efficient ANOVA for directional data. ANNALS OF THE INSTITUTE OF STATISTICAL MATHEMATICS, 69(1), 39–62.
Vancouver
1.
Ley C, Swan Y, Verdebout T. Efficient ANOVA for directional data. ANNALS OF THE INSTITUTE OF STATISTICAL MATHEMATICS. 2017;69(1):39–62.
MLA
Ley, Christophe, Yvik Swan, and Thomas Verdebout. “Efficient ANOVA for Directional Data.” ANNALS OF THE INSTITUTE OF STATISTICAL MATHEMATICS 69.1 (2017): 39–62. Print.