Testing Group Symmetry of a Multivariate Distribution
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....
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| Format: | Article |
| Language: | English |
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MDPI AG
2009-11-01
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| Series: | Symmetry |
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| Online Access: | http://www.mdpi.com/2073-8994/1/2/180/ |
| _version_ | 1798038387993608192 |
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| author | Lyudmila Sakhanenko |
| author_facet | Lyudmila Sakhanenko |
| author_sort | Lyudmila Sakhanenko |
| collection | DOAJ |
| description | 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. |
| first_indexed | 2024-04-11T21:39:31Z |
| format | Article |
| id | doaj.art-81fb59db6c6946a6aa4dd4a46b0af9fd |
| institution | Directory Open Access Journal |
| issn | 2073-8994 |
| language | English |
| last_indexed | 2024-04-11T21:39:31Z |
| publishDate | 2009-11-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Symmetry |
| spelling | doaj.art-81fb59db6c6946a6aa4dd4a46b0af9fd2022-12-22T04:01:39ZengMDPI AGSymmetry2073-89942009-11-011218020010.3390/sym1020180Testing Group Symmetry of a Multivariate DistributionLyudmila SakhanenkoWe 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.http://www.mdpi.com/2073-8994/1/2/180/symmetric distributionsDonsker classlinear operator |
| spellingShingle | Lyudmila Sakhanenko Testing Group Symmetry of a Multivariate Distribution Symmetry symmetric distributions Donsker class linear operator |
| title | Testing Group Symmetry of a Multivariate Distribution |
| title_full | Testing Group Symmetry of a Multivariate Distribution |
| title_fullStr | Testing Group Symmetry of a Multivariate Distribution |
| title_full_unstemmed | Testing Group Symmetry of a Multivariate Distribution |
| title_short | Testing Group Symmetry of a Multivariate Distribution |
| title_sort | testing group symmetry of a multivariate distribution |
| topic | symmetric distributions Donsker class linear operator |
| url | http://www.mdpi.com/2073-8994/1/2/180/ |
| work_keys_str_mv | AT lyudmilasakhanenko testinggroupsymmetryofamultivariatedistribution |