Tests and estimates of shape based on spatial signs and ranks

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dc.contributor.author Sirkiä, Seija
dc.contributor.author Taskinen, Sara
dc.contributor.author Oja, Hannu
dc.contributor.author Tyler, David
dc.date.accessioned 2012-11-30T12:20:47Z
dc.date.available 2012-11-30T12:20:47Z
dc.date.issued 2009 fi
dc.identifier.citation Sirkiä, S., Taskinen, S., Oja, H., & Tyler, D. (2009). Tests and estimates of shape based on spatial signs and ranks. J. Nonparametr. Stat., 21 (2), 155-176. doi:10.1080/10485250802495691 fi
dc.identifier.issn 1048-5252
dc.identifier.other TUTKAID_31980
dc.identifier.uri http://hdl.handle.net/123456789/40495
dc.description.abstract Nonparametric procedures for testing and estimation of the shape matrix in the case of multivariate elliptic distribution are considered. Testing for sphericity is an important special case. The tests and estimates are based on the spatial sign and rank covariance matrices. The estimates based on the spatial sign covariance matrix and symmetrized spatial sign covariance matrix are Tyler's [A distribution-free M-estimator of multivariate scatter, Ann. Statist. 15 (1987), pp. 234–251] shape matrix and and Dümbgen's [On Tyler's M-functional of scatter in high dimension, Ann. Inst. Statist. Math. 50 (1998), pp. 471–491] shape matrix, respectively. The test based on the spatial sign covariance matrix is the sign test statistic in the class of nonparametric tests proposed by Hallin and Paindaveine [Semiparametrically efficient rank-based inference for shape. I. Optimal rank-based tests for sphericity, Ann. Statist. 34 (2006), pp. 2707–2756]. New tests and estimates based on the spatial rank covariance matrix are proposed. The shape estimates introduced in the paper play an important role in the inner standardisation of the spatial sign and rank tests for multivariate location. Limiting distributions of the tests and estimates are reviewed and derived, and asymptotic efficiencies as well as finite-sample efficiencies of the proposed tests are compared with those of the classical modified John's [Some optimal multivariate tests, Biometrika 58 (1971), pp. 123–127; The distribution of a statistic used for testing sphericity of normal distributions, Biometrika 59 (1972), pp. 169–173] test and the van der Waerden test (Hallin and Paindaveine, [Semiparametrically efficient rank-based inference for shape. I. Optimal rank-based tests for sphericity, Ann. Statist. 34 (2006), pp. 2707–2756]). The symmetrised spatial sign- and rank-based estimates and tests seem to have a very high efficiency in the multivariate normal case, and they are much better than the classical estimate (shape matrix based on the regular covariance matrix) and test (John's test) for distributions with heavy tails. fi
dc.language.iso eng
dc.publisher Taylor & Francis
dc.relation.ispartof Journal of Nonparametric Statistics
dc.rights © Taylor & Francis. This is an author's final draft version of an article whose final and definitive form has been published by Taylor & Francis.
dc.subject.other moniulotteiset merkki- ja jarjestysluvut fi
dc.title Tests and estimates of shape based on spatial signs and ranks fi
dc.type Article en
dc.identifier.urn URN:NBN:fi:jyu-201211293123
dc.subject.kota 112
dc.contributor.laitos Matematiikan ja tilastotieteen laitos fi
dc.contributor.laitos Department of Mathematics and Statistics en
dc.contributor.oppiaine tilastotiede fi
jyx.tutka.volyme 21
jyx.tutka.mnumber 2
jyx.tutka.pagetopage 155-176
dc.type.uri http://purl.org/eprint/type/SubmittedJournalArticle
dc.identifier.doi 10.1080/10485250802495691
dc.date.updated 2012-11-29T10:39:57Z
dc.description.version Author's Final draft
eprint.status http://purl.org/eprint/type/status/PeerReviewed

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