Depth-based runs tests for bivariate central symmetry - Kölner UniversitätsPublikationsServer

Dyckerhoff, Rainer, Ley, Christophe ORCID: 0000-0002-2290-8437 and Paindaveine, Davy (2015). Depth-based runs tests for bivariate central symmetry. Ann. Inst. Stat. Math., 67 (5). S. 917 - 942. HEIDELBERG: SPRINGER HEIDELBERG. ISSN 1572-9052

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DOI:10.1007/s10463-014-0480-y

Abstract

McWilliams (J Am Stat Assoc 85:1130-1133, 1990) introduced a nonparametric procedure based on runs for the problem of testing univariate symmetry about the origin (equivalently, about an arbitrary specified center). His procedure first reorders the observations according to their absolute values, then rejects the null when the number of runs in the resulting series of signs is too small. This test is universally consistent and enjoys good robustness properties, but is unfortunately limited to the univariate setup. In this paper, we extend McWilliams' procedure into tests of bivariate central symmetry. The proposed tests first reorder the observations according to their statistical depth in a symmetrized version of the sample, then reject the null when an original concept of simplicial runs is too small. Our tests are affine invariant and have good robustness properties. In particular, they do not require any finite moment assumption. We derive their limiting null distribution, which establishes their asymptotic distribution freeness. We study their finite-sample properties through Monte Carlo experiments and conclude with some final comments.

Item Type:

Journal Article

Creators:

Creators	Email	ORCID	ORCID Put Code
Dyckerhoff, Rainer	UNSPECIFIED	UNSPECIFIED	UNSPECIFIED
Ley, Christophe	UNSPECIFIED	orcid.org/0000-0002-2290-8437	UNSPECIFIED
Paindaveine, Davy	UNSPECIFIED	UNSPECIFIED	UNSPECIFIED