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dc.contributor.authorZollanvari, Amin
dc.contributor.authorGenton, Marc G.
dc.date.accessioned2015-08-03T11:05:06Z
dc.date.available2015-08-03T11:05:06Z
dc.date.issued2013-05-23
dc.identifier.issn09727671
dc.identifier.pmid24288447
dc.identifier.doi10.1007/s13171-013-0029-9
dc.identifier.urihttp://hdl.handle.net/10754/562770
dc.description.abstractWe provide a fundamental theorem that can be used in conjunction with Kolmogorov asymptotic conditions to derive the first moments of well-known estimators of the actual error rate in linear discriminant analysis of a multivariate Gaussian model under the assumption of a common known covariance matrix. The estimators studied in this paper are plug-in and smoothed resubstitution error estimators, both of which have not been studied before under Kolmogorov asymptotic conditions. As a result of this work, we present an optimal smoothing parameter that makes the smoothed resubstitution an unbiased estimator of the true error. For the sake of completeness, we further show how to utilize the presented fundamental theorem to achieve several previously reported results, namely the first moment of the resubstitution estimator and the actual error rate. We provide numerical examples to show the accuracy of the succeeding finite sample approximations in situations where the number of dimensions is comparable or even larger than the sample size.
dc.publisherSpringer Science and Business Media LLC
dc.relation.urlhttp://www.ncbi.nlm.nih.gov/pmc/articles/PMC3840470
dc.relation.urlhttp://europepmc.org/articles/pmc3840470?pdf=render
dc.rightsArchived with thanks to Springer Science and Business Media LLC
dc.rightsThis file is an open access version redistributed from: http://europepmc.org/articles/pmc3840470?pdf=render
dc.titleOn Kolmogorov asymptotics of estimators of the misclassification error rate in linear discriminant analysis
dc.typeArticle
dc.contributor.departmentApplied Mathematics and Computational Science Program
dc.contributor.departmentComputer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division
dc.contributor.departmentSpatio-Temporal Statistics and Data Analysis Group
dc.contributor.departmentStatistics Program
dc.identifier.journalSankhya: The Indian Journal of Statistics
dc.identifier.pmcidPMC3840470
dc.rights.embargodate2014-05-23
dc.eprint.versionPost-print
dc.contributor.institutionDepartment of Statistics, Department of Electrical and Computer Engineering, Texas A and M University, College Station, TX 77843, United States
kaust.personGenton, Marc G.
refterms.dateFOA2020-04-19T14:58:53Z
dc.date.published-online2013-05-24
dc.date.published-print2013-08


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