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dc.contributor.authorNordhausen, Klaus
dc.contributor.authorOja, Hannu
dc.contributor.authorTyler, David E.
dc.date.accessioned2021-12-20T12:12:36Z
dc.date.available2021-12-20T12:12:36Z
dc.date.issued2022
dc.identifier.citationNordhausen, K., Oja, H., & Tyler, D. E. (2022). Asymptotic and bootstrap tests for subspace dimension. <i>Journal of Multivariate Analysis</i>, <i>188</i>, Article 104830. <a href="https://doi.org/10.1016/j.jmva.2021.104830" target="_blank">https://doi.org/10.1016/j.jmva.2021.104830</a>
dc.identifier.otherCONVID_101039114
dc.identifier.urihttps://jyx.jyu.fi/handle/123456789/79046
dc.description.abstractMany linear dimension reduction methods proposed in the literature can be formulated using an appropriate pair of scatter matrices. The eigen-decomposition of one scatter matrix with respect to another is then often used to determine the dimension of the signal subspace and to separate signal and noise parts of the data. Three popular dimension reduction methods, namely principal component analysis (PCA), fourth order blind identification (FOBI) and sliced inverse regression (SIR) are considered in detail and the first two moments of subsets of the eigenvalues are used to test for the dimension of the signal space. The limiting null distributions of the test statistics are discussed and novel bootstrap strategies are suggested for the small sample cases. In all three cases, consistent test-based estimates of the signal subspace dimension are introduced as well. The asymptotic and bootstrap tests are illustrated in real data examples.en
dc.format.mimetypeapplication/pdf
dc.language.isoeng
dc.publisherElsevier
dc.relation.ispartofseriesJournal of Multivariate Analysis
dc.rightsCC BY 4.0
dc.subject.otherOrder determination
dc.subject.otherPrincipal component analysis
dc.subject.otherSliced inverse regression
dc.titleAsymptotic and bootstrap tests for subspace dimension
dc.typearticle
dc.identifier.urnURN:NBN:fi:jyu-202112206029
dc.contributor.laitosMatematiikan ja tilastotieteen laitosfi
dc.contributor.laitosDepartment of Mathematics and Statisticsen
dc.type.urihttp://purl.org/eprint/type/JournalArticle
dc.description.reviewstatuspeerReviewed
dc.relation.issn0047-259X
dc.relation.volume188
dc.type.versionpublishedVersion
dc.rights.copyright© 2021 the Authors
dc.rights.accesslevelopenAccessfi
dc.subject.ysomonimuuttujamenetelmät
dc.subject.ysoriippumattomien komponenttien analyysi
dc.subject.ysoestimointi
dc.format.contentfulltext
jyx.subject.urihttp://www.yso.fi/onto/yso/p2131
jyx.subject.urihttp://www.yso.fi/onto/yso/p38529
jyx.subject.urihttp://www.yso.fi/onto/yso/p11349
dc.rights.urlhttps://creativecommons.org/licenses/by/4.0/
dc.relation.doi10.1016/j.jmva.2021.104830
jyx.fundinginformationDavid E. Tyler’s research was partially supported by the National Science FoundationGrant No. DMS-1407751.


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