Common Multivariate Estimators of Location and Scatter Capture the Symmetry of the Underlying Distribution

0504387 - ÚI 2022 RIV US eng J - Journal Article
Kalina, Jan
Common Multivariate Estimators of Location and Scatter Capture the Symmetry of the Underlying Distribution.
Communications in Statistics - Simulation and Computation. Roč. 50, č. 10 (2021), s. 2845-2857. ISSN 0361-0918. E-ISSN 1532-4141
Grant - others:GA ČR(CZ) GA17-07384S
Institutional support: RVO:67985807
Keywords : multivariate estimation * symmetry test * robust estimation * scatter estimator * axial symmetry
OECD category: Statistics and probability
Impact factor: 1.162, year: 2021
Method of publishing: Limited access
http://dx.doi.org/10.1080/03610918.2019.1615624

The article discusses how various multivariate location and scatter estimators capture the symmetry of the underlying distribution. Very general sufficient conditions are formulated, which ensure various symmetry properties of functionals corresponding to location or scatter. Examples of robust multivariate estimators, which fulfill these conditions, are discussed in detail. The obtained symmetry of the estimators is applicable to hypothesis tests of symmetry of the underlying distribution of the multivariate data. For this task, we propose to perform permutation tests exploiting the nonparametric combination methodology. The performance of the newly proposed tests is illustrated on simulated as well as real data. The tests are suitable for small sample sizes and represent the first available symmetry tests suitable also for non-elliptical distributions and for more than just two variables.
Permanent Link: http://hdl.handle.net/11104/0296031