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dc.contributor.authorRadojičić, Una
dc.contributor.authorNordhausen, Klaus
dc.contributor.authorVirta, Joni
dc.date.accessioned2022-01-05T10:09:30Z
dc.date.available2022-01-05T10:09:30Z
dc.date.issued2021
dc.identifier.citationRadojičić, U., Nordhausen, K., & Virta, J. (2021). Large-sample properties of unsupervised estimation of the linear discriminant using projection pursuit. <i>Electronic Journal of Statistics</i>, <i>15</i>(2), 6677-6739. <a href="https://doi.org/10.1214/21-EJS1956" target="_blank">https://doi.org/10.1214/21-EJS1956</a>
dc.identifier.otherCONVID_103549585
dc.identifier.urihttps://jyx.jyu.fi/handle/123456789/79240
dc.description.abstractWe study the estimation of the linear discriminant with projection pursuit, a method that is unsupervised in the sense that it does not use the class labels in the estimation. Our viewpoint is asymptotic and, as our main contribution, we derive central limit theorems for estimators based on three different projection indices, skewness, kurtosis, and their convex combination. The results show that in each case the limiting covariance matrix is proportional to that of linear discriminant analysis (LDA), a supervised estimator of the discriminant. An extensive comparative study between the asymptotic variances reveals that projection pursuit gets arbitrarily close in efficiency to LDA when the distance between the groups is large enough and their proportions are reasonably balanced. Additionally, we show that consistent unsupervised estimation of the linear discriminant can be achieved also in high-dimensional regimes where the dimension grows at a suitable rate to the sample size, for example, pn=o(n1∕3) is sufficient under skewness-based projection pursuit. We conclude with a real data example and a simulation study investigating the validity of the obtained asymptotic formulas for finite samples.en
dc.format.mimetypeapplication/pdf
dc.language.isoeng
dc.publisherInstitute of Mathematical Statistics
dc.relation.ispartofseriesElectronic Journal of Statistics
dc.rightsCC BY 4.0
dc.subject.otherclustering
dc.subject.otherkurtosis
dc.subject.otherlinear discriminant analysis
dc.subject.otherprojection pursuit
dc.subject.otherskewness
dc.titleLarge-sample properties of unsupervised estimation of the linear discriminant using projection pursuit
dc.typearticle
dc.identifier.urnURN:NBN:fi:jyu-202201051019
dc.contributor.laitosMatematiikan ja tilastotieteen laitosfi
dc.contributor.laitosDepartment of Mathematics and Statisticsen
dc.contributor.oppiaineTilastotiedefi
dc.contributor.oppiaineStatisticsen
dc.type.urihttp://purl.org/eprint/type/JournalArticle
dc.description.reviewstatuspeerReviewed
dc.format.pagerange6677-6739
dc.relation.issn1935-7524
dc.relation.numberinseries2
dc.relation.volume15
dc.type.versionpublishedVersion
dc.rights.copyright© Authors, 2021
dc.rights.accesslevelopenAccessfi
dc.subject.ysomatematiikka
dc.subject.ysoestimointi
dc.format.contentfulltext
jyx.subject.urihttp://www.yso.fi/onto/yso/p3160
jyx.subject.urihttp://www.yso.fi/onto/yso/p11349
dc.rights.urlhttps://creativecommons.org/licenses/by/4.0/
dc.relation.doi10.1214/21-EJS1956
jyx.fundinginformationThe work of Joni Virta was supported by the Academy of Finland (Grant 335077).


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