Näytä suppeat kuvailutiedot

dc.contributor.authorSirkiä, Seija
dc.contributor.authorTaskinen, Sara
dc.contributor.authorOja, Hannu
dc.contributor.authorTyler, David
dc.date.accessioned2012-11-30T12:20:47Z
dc.date.available2012-11-30T12:20:47Z
dc.date.issued2009fi
dc.identifier.citationSirkiä, S., Taskinen, S., Oja, H., & Tyler, D. (2009). Tests and estimates of shape based on spatial signs and ranks. <em>J. Nonparametr. Stat.</em>, 21 (2), 155-176. <a href="http://dx.doi.org/10.1080/10485250802495691">doi:10.1080/10485250802495691</a>fi
dc.identifier.otherTUTKAID_31980
dc.identifier.urihttps://jyx.jyu.fi/handle/123456789/40495
dc.description.abstractNonparametric 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.isoeng
dc.publisherTaylor & Francis
dc.relation.ispartofseriesJournal of Nonparametric Statistics
dc.subject.othermoniulotteiset merkki- ja jarjestysluvutfi
dc.titleTests and estimates of shape based on spatial signs and ranksfi
dc.typeArticle
dc.identifier.urnURN:NBN:fi:jyu-201211293123
dc.contributor.laitosMatematiikan ja tilastotieteen laitosfi
dc.contributor.laitosDepartment of Mathematics and Statisticsen
dc.contributor.oppiaineTilastotiedefi
dc.type.urihttp://purl.org/eprint/type/SubmittedJournalArticle
dc.identifier.doi10.1080/10485250802495691
dc.date.updated2012-11-29T10:39:57Z
dc.type.coarjournal article
dc.description.reviewstatuspeerReviewed
dc.format.pagerange155-176
dc.relation.issn1048-5252
dc.relation.numberinseries2
dc.relation.volume21
dc.type.versionacceptedVersion
dc.rights.copyright© 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.rights.accesslevelopenAccessfi


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