Symmetry 2009, 1(2), 180-200; doi:10.3390/sym1020180

Testing Group Symmetry of a Multivariate Distribution

Received: 15 September 2009; Accepted: 24 November 2009 / Published: 26 November 2009
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Abstract: We propose and study a general class of tests for group symmetry of a multivariate distribution, which encompasses different types of symmetry, such as ellipsoidal and permutation symmetries among others. Our approach is based on supremum norms of special empirical processes combined with bootstrap. We show that these tests are consistent against any fixed alternative. This work generalizes the methodology of Koltchinskii and Sakhanenko [7], developed for ellipsoidal symmetry to the case of group symmetry. It also provides a unified approach to testing different types of symmetry of a multivariate distribution.
Keywords: symmetric distributions; Donsker class; linear operator
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MDPI and ACS Style

Sakhanenko, L. Testing Group Symmetry of a Multivariate Distribution. Symmetry 2009, 1, 180-200.

AMA Style

Sakhanenko L. Testing Group Symmetry of a Multivariate Distribution. Symmetry. 2009; 1(2):180-200.

Chicago/Turabian Style

Sakhanenko, Lyudmila. 2009. "Testing Group Symmetry of a Multivariate Distribution." Symmetry 1, no. 2: 180-200.

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