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dc.contributor.author Devroye, Luc
dc.contributor.author Györfi, László
dc.contributor.author Lugosi, Gábor
dc.contributor.author Walk, Harro
dc.date.accessioned 2020-06-02T08:59:26Z
dc.date.available 2020-06-02T08:59:26Z
dc.date.issued 2018
dc.identifier.citation Devroye L, Györfi L, Lugosi G, Walk H. A nearest neighbor estimate of the residual variance. Electron J Stat. 2018 Jun 6;12(1):1752-78. DOI: 10.1214/18-EJS1438
dc.identifier.issn 1935-7524
dc.identifier.uri http://hdl.handle.net/10230/44868
dc.description.abstract We study the problem of estimating the smallest achievable mean-squared error in regression function estimation. The problem is equivalent to estimating the second moment of the regression function of Y on X∈Rd. We introduce a nearest-neighbor-based estimate and obtain a normal limit law for the estimate when X has an absolutely continuous distribution, without any condition on the density. We also compute the asymptotic variance explicitly and derive a non-asymptotic bound on the variance that does not depend on the dimension d. The asymptotic variance does not depend on the smoothness of the density of X or of the regression function. A non-asymptotic exponential concentration inequality is also proved. We illustrate the use of the new estimate through testing whether a component of the vector X carries information for predicting Y.
dc.description.sponsorship Luc Devroye was supported by the Natural Sciences and Engineering Research Council (NSERC) of Canada. László Györfi was supported by the National University of Public Service under the priority project KOFOP-2.1.2-VEKOP-15-2016-00001 titled "Public Service Development Establishing Good Governance” in the Ludovika Workshop. Gábor Lugosi was supported by the Spanish Ministry of Economy and Competitiveness, Grant MTM2015-67304-P and FEDER, EU.
dc.format.mimetype application/pdf
dc.language.iso eng
dc.publisher The Institute of Mathematical Statistics and the Bernoulli Society
dc.relation.ispartof Electronic Journal of Statistics. 2018 Jun 6;12(1):1752-78
dc.rights Copyright for all articles in EJP is CC BY 4.0.
dc.rights.uri https://creativecommons.org/licenses/by/4.0/
dc.title A nearest neighbor estimate of the residual variance
dc.type info:eu-repo/semantics/article
dc.identifier.doi http://dx.doi.org/10.1214/18-EJS1438
dc.subject.keyword Regression functional
dc.subject.keyword Nearest-neighbor-based estimate
dc.subject.keyword Asymptotic normality
dc.subject.keyword Concentration inequalities
dc.subject.keyword Dimension reduction
dc.relation.projectID info:eu-repo/grantAgreement/ES/1PE/MTM2015-67304-P
dc.rights.accessRights info:eu-repo/semantics/openAccess
dc.type.version info:eu-repo/semantics/publishedVersion

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