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Asymptotic properties of the misclassification rates for Euclidean Distance Discriminant rule in high-dimensional data
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematical Statistics.
2015 (English)In: Journal of Multivariate Analysis, ISSN 0047-259X, E-ISSN 1095-7243, Vol. 140, 234-244 p.Article in journal (Refereed) Published
Abstract [en]

Performance accuracy of the Euclidean Distance Discriminant rule (EDDR) is studied in the high-dimensional asymptotic framework which allows the dimensionality to exceed sample size. Under mild assumptions on the traces of the covariance matrix, our new results provide the asymptotic distribution of the conditional misclassification rate and the explicit expression for the consistent and asymptotically unbiased estimator of the expected misclassification rate. To get these properties, new results on the asymptotic normality of the quadratic forms and traces of the higher power of Wishart matrix, are established. Using our asymptotic results, we further develop two generic methods of determining a cut-off point for EDDR to adjust the misclassification rates. Finally, we numerically justify the high accuracy of our asymptotic findings along with the cut-off determination methods in finite sample applications, inclusive of the large sample and high-dimensional scenarios.

Place, publisher, year, edition, pages
2015. Vol. 140, 234-244 p.
Keyword [en]
High-dimensional framework, Conditional error rate, Expected error rate
National Category
URN: urn:nbn:se:kth:diva-173140DOI: 10.1016/j.jmva.2015.05.008ISI: 000359033100017ScopusID: 2-s2.0-84935912391OAI: diva2:854941
Swedish Research CouncilThe Royal Swedish Academy of Sciences

QC 20150918

Available from: 2015-09-18 Created: 2015-09-07 Last updated: 2015-09-18Bibliographically approved

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Pavlenko, Tatjana
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