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A U-classifier for high-dimensional data under non-normality
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.).ORCID iD: 0000-0002-0633-5579
2018 (English)In: Journal of Multivariate Analysis, ISSN 0047-259X, E-ISSN 1095-7243, Vol. 167, p. 269-283Article in journal (Refereed) Published
Abstract [en]

A classifier for two or more samples is proposed when the data are high-dimensional and the distributions may be non-normal. The classifier is constructed as a linear combination of two easily computable and interpretable components, the U-component and the P-component. The U-component is a linear combination of U-statistics of bilinear forms of pairwise distinct vectors from independent samples. The P-component, the discriminant score, is a function of the projection of the U-component on the observation to be classified. Together, the two components constitute an inherently bias-adjusted classifier valid for high-dimensional data. The classifier is linear but its linearity does not rest on the assumption of homoscedasticity. Properties of the classifier and its normal limit are given under mild conditions. Misclassification errors and asymptotic properties of their empirical counterparts are discussed. Simulation results are used to show the accuracy of the proposed classifier for small or moderate sample sizes and large dimensions. Applications involving real data sets are also included. 

Place, publisher, year, edition, pages
Uppsala Univ, Dept Stat, Uppsala, Sweden. KTH, Royal Inst Technol, Dept Math, Stockholm, Sweden.: ELSEVIER INC , 2018. Vol. 167, p. 269-283
Keywords [en]
Bias-adjusted classifier, High-dimensional classification, U-statistics
National Category
Mathematics
Identifiers
URN: urn:nbn:se:kth:diva-233587DOI: 10.1016/j.jmva.2018.05.008ISI: 000441371100017Scopus ID: 2-s2.0-85047908288OAI: oai:DiVA.org:kth-233587DiVA, id: diva2:1242378
Note

QC 20180828

Available from: 2018-08-28 Created: 2018-08-28 Last updated: 2018-09-03Bibliographically approved

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Pavlenko, Tatjana

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CiteExportLink to record
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Citation style
  • apa
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  • vancouver
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  • de-DE
  • en-GB
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  • nn-NO
  • nn-NB
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  • Other locale
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Output format
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