On Kolmogorov asymptotics of estimators of the misclassification error rate in linear discriminant analysis

Handle URI:
http://hdl.handle.net/10754/562770
Title:
On Kolmogorov asymptotics of estimators of the misclassification error rate in linear discriminant analysis
Authors:
Zollanvari, Amin; Genton, Marc G. ( 0000-0001-6467-2998 )
Abstract:
We 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.
KAUST Department:
Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division; Applied Mathematics and Computational Science Program; Spatio-Temporal Statistics and Data Analysis Group
Publisher:
Springer Verlag
Journal:
Sankhya: The Indian Journal of Statistics
Issue Date:
24-May-2013
DOI:
10.1007/s13171-013-0029-9
PubMed ID:
24288447
PubMed Central ID:
PMC3840470
Type:
Article
ISSN:
09727671
Additional Links:
http://www.ncbi.nlm.nih.gov/pmc/articles/PMC3840470
Appears in Collections:
Articles; Applied Mathematics and Computational Science Program; Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division

Full metadata record

DC FieldValue Language
dc.contributor.authorZollanvari, Aminen
dc.contributor.authorGenton, Marc G.en
dc.date.accessioned2015-08-03T11:05:06Zen
dc.date.available2015-08-03T11:05:06Zen
dc.date.issued2013-05-24en
dc.identifier.issn09727671en
dc.identifier.pmid24288447en
dc.identifier.doi10.1007/s13171-013-0029-9en
dc.identifier.urihttp://hdl.handle.net/10754/562770en
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.en
dc.publisherSpringer Verlagen
dc.relation.urlhttp://www.ncbi.nlm.nih.gov/pmc/articles/PMC3840470en
dc.titleOn Kolmogorov asymptotics of estimators of the misclassification error rate in linear discriminant analysisen
dc.typeArticleen
dc.contributor.departmentComputer, Electrical and Mathematical Sciences and Engineering (CEMSE) Divisionen
dc.contributor.departmentApplied Mathematics and Computational Science Programen
dc.contributor.departmentSpatio-Temporal Statistics and Data Analysis Groupen
dc.identifier.journalSankhya: The Indian Journal of Statisticsen
dc.identifier.pmcidPMC3840470en
dc.contributor.institutionDepartment of Statistics, Department of Electrical and Computer Engineering, Texas A and M University, College Station, TX 77843, United Statesen
kaust.authorGenton, Marc G.en

Related articles on PubMed

All Items in KAUST are protected by copyright, with all rights reserved, unless otherwise indicated.