Efficient ANOVA for directional data

Ley, Christophe; Swan, Yves-Caoimhin; Verdebout, Thomas

doi:10.1007/s10463-015-0533-x

Cited by 10 publications

(5 citation statements)

References 37 publications

(38 reference statements)

Supporting

Mentioning

Contrasting

Order By: Relevance

“…We conclude this section by attracting the reader's attention to the fact that this multi‐sample problem here complements, for the FvML case, the analysis of variance study in Ley et al . ().…”

Section: Multi‐sample Tests On the Equality Of Concentrationsmentioning

confidence: 97%

See 1 more Smart Citation

Local Powers of Optimal One‐sample and Multi‐sample Tests for the Concentration of Fisher‐von Mises‐Langevin Distributions

Ley

Verdebout

2014

Int Statistical Rev

Self Cite

View full text Add to dashboard Cite

One-sample and multi-sample tests on the concentration parameter of Fisher-von Mises-Langevin (FvML) distributions on (hyper-)spheres have been well studied in the literature. However, only little is known about their behavior under local alternatives, which is due to complications inherent to the curved nature of the parameter space. The aim of the present paper therefore consists in filling that gap by having recourse to the Le Cam methodol- * E-mail address: chrisley@ulb.ac.be; URL: http://homepages.ulb.ac.be/˜chrisley, address:

show abstract

Section: Multi‐sample Tests On the Equality Of Concentrationsmentioning

confidence: 97%

“…A more general version of this property, in the case of m independent populations, has allowed Ley et al . () to propose efficient analysis of variance for directional distributions.…”

Section: Introductionmentioning

confidence: 99%

Local Powers of Optimal One‐sample and Multi‐sample Tests for the Concentration of Fisher‐von Mises‐Langevin Distributions

Ley

Verdebout

2014

Int Statistical Rev

Self Cite

View full text Add to dashboard Cite

show abstract

“…Ley et al (2015) investigated the high dimensional robustness of Watson's test for the mean direction. Paindaveine and Verdebout (2015) proposed optimal rank-based tests for the mean direction, and Ley et al (2017) used the invariance principle to construct rank-based semi-parametric tests for the homogeneity of mean directions. Paindaveine and Verdebout (2017) investigated the problem of testing for a specified mean direction when the underlying distribution tends to uniformity.…”

Section: Location and Concentrationmentioning

confidence: 99%

Recent advances in directional statistics

Pewsey

García‐Portugués

2021

TEST

View full text Add to dashboard Cite

Mainstream statistical methodology is generally applicable to data observed in Euclidean space. There are, however, numerous contexts of considerable scientific interest in which the natural supports for the data under consideration are Riemannian manifolds like the unit circle, torus, sphere, and their extensions. Typically, such data can be represented using one or more directions, and directional statistics is the branch of statistics that deals with their analysis. In this paper, we provide a review of the many recent developments in the field since the publication of Mardia and Jupp (Wiley 1999), still the most comprehensive text on directional statistics. Many of those developments have been stimulated by interesting applications in fields as diverse as astronomy, medicine, genetics, neurology, space situational awareness, acoustics, image analysis, text mining, environmetrics, and machine learning. We begin by considering developments for the exploratory analysis of directional data before progressing to distributional models, general approaches to inference, hypothesis testing, regression, nonparametric curve estimation, methods for dimension reduction, classification and clustering, and the modelling of time series, spatial and spatio-temporal data. AnWe are most grateful to three anonymous referees and, in alphabetical order, to

show abstract

“…Recently, Ley et al . (2017) derived a theoretically elegant and practically promising uniform locally and asymptotically normal (ULAN) test, based on LeCam methodology. They also proposed its rank‐based version that is robust under the class of rotationally symmetric distributions.…”

Section: Introductionmentioning

confidence: 99%

An Efficient Test for Homogeneity of Mean Directions on the Hyper‐sphere

Kulkarni

SenGupta

2021

Int Statistical Rev

View full text Add to dashboard Cite

Summary The paper aims to develop a universally implementable efficient test for testing homogeneity of mean directions of several independent hyper‐spherical populations. Conventional tests are valid only under highly concentrated and/or large‐size groups. Focusing on the popular Langevin distribution on a d‐hyper‐sphere, the present work extends the very recent results for the circular case. The hurdle of the nuisance non‐location‐scale concentration parameter κ is overcome through a variant of the integrated likelihood ratio test (ILRT), yielding a simple and elegant test statistic. Analytically, second‐order accurate asymptotic chi‐squared distribution of ILRT is established. Extensive simulation study demonstrates that ILRT uniformly outperforms its peers, notably under highly dispersed groups, which is precisely the target parametric region, and is robust under a large class of alternate distributions. Five real‐life data analyses from diverse disciplines, including the emerging field of vectorcardiography and a novel application to compositional data analysis in the context of drug development, illustrate applications of the findings.

show abstract

Efficient ANOVA for directional data

Cited by 10 publications

References 37 publications

Local Powers of Optimal One‐sample and Multi‐sample Tests for the Concentration of Fisher‐von Mises‐Langevin Distributions

Local Powers of Optimal One‐sample and Multi‐sample Tests for the Concentration of Fisher‐von Mises‐Langevin Distributions

Recent advances in directional statistics

An Efficient Test for Homogeneity of Mean Directions on the Hyper‐sphere

Contact Info

Product

Resources

About