Optimal tests for elliptical symmetry: specified and unspecified location

Sladana Babic, Laetitia Gelbgras, Marc Hallin and Christophe Ley

No 2019-26, Working Papers ECARES from ULB -- Universite Libre de Bruxelles

Abstract: Although the assumption of elliptical symmetry is quite common in multivariate analysis and widespread in a number of applications, the problem of testing the null hypothesis of ellipticity so far has not been addressed in a fully satisfactory way. Most of the literature in the area indeed addresses the null hypothesis of elliptical symmetry with specified location and actually addresses location rather than non-elliptical alternatives. In thi spaper, we are proposing new classes of testing procedures,both for specified and unspecified location. The backbone of our construction is Le Cam’s asymptotic theory of statistical experiments, and optimality is to be understood locally and asymptotically within the family of generalized skew-elliptical distributions. The tests we are proposing are meeting all the desired properties of a “good” test of elliptical symmetry:they have a simple asymptotic distribution under the entire null hypothesis of elliptical symmetry with unspecified radial density and shape parameter; they are affine-invariant, computationally fast, intuitively understandable, and not too demanding in terms of moments. While achieving optimality against generalized skew-elliptical alternatives, they remain quite powerful under a much broader class of non-elliptical distributions and significantly outperform the available competitors

Keywords: Elliptical Symmetry; Local Asymptotic normality; Maximin tests; Multivariate skewness; semiparametric inference; skew-elliptical densities (search for similar items in EconPapers)
Pages: 41 p.
Date: 2019-11
New Economics Papers: this item is included in nep-ecm
References: View references in EconPapers View complete reference list from CitEc
Citations:

Published by:

Downloads: (external link)
https://dipot.ulb.ac.be/dspace/bitstream/2013/2959 ... LLIN_LEY-optimal.pdf Full text for the whole work, or for a work part (application/pdf)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:eca:wpaper:2013/295909

Ordering information: This working paper can be ordered from
http://hdl.handle.ne ... lb.ac.be:2013/295909

Access Statistics for this paper

More papers in Working Papers ECARES from ULB -- Universite Libre de Bruxelles Contact information at EDIRC.
Bibliographic data for series maintained by Benoit Pauwels (bpauwels@ulb.ac.be).