Article (Scientific journals)
Distribution under elliptical symmetry of a distance-based multivariate coefficient of variation
Aerts, Stéphanie; Haesbroeck, Gentiane; Ruwet, Christel
2018In Statistical Papers
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Keywords :
Bias reduction; Coefficient of variation; Decentralized F-distribution
Disciplines :
Mathematics
Author, co-author :
Aerts, Stéphanie ;  Université de Liège - ULiège > HEC-Ecole de gestion : UER > UER Opérations : Informatique de gestion
Haesbroeck, Gentiane ;  Université de Liège - ULiège > Département de mathématique > Statistique mathématique
Ruwet, Christel ;  Université de Liège - ULiège > Département de mathématique > Statistique mathématique
Language :
English
Title :
Distribution under elliptical symmetry of a distance-based multivariate coefficient of variation
Publication date :
2018
Journal title :
Statistical Papers
ISSN :
0932-5026
Publisher :
Springer Science & Business Media B.V.
Peer reviewed :
Peer Reviewed verified by ORBi
Name of the research project :
Robust multivariate dispersion measures
Funders :
IAP Research Network P7/06 of the Belgian State.
Commentary :
In the univariate setting, the coefficient of variation is widely used to measure the relative dispersion of a random variable with respect to its mean. Several extensions of the univariate coefficient of variation to the multivariate setting have been introduced in the literature. In this paper, we focus on a distance-based multivariate coefficient of variation. First, some real examples are discussed to motivate the use of the considered multivariate dispersion measure. Then, the asymptotic distribution of several estimators is analyzed under elliptical symmetry and used to construct approximate parametric confidence intervals that are compared with non-parametric intervals in a simulation study. Under normality, the exact distribution of the classical estimator is derived. As this natural estimator is biased, some bias corrections are proposed and compared by means of simulations.
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