A nearest neighbor estimate of the residual variance

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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.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.en
• 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.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.doi http://dx.doi.org/10.1214/18-EJS1438
• dc.identifier.issn 1935-7524
• dc.identifier.uri http://hdl.handle.net/10230/44868
• 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.relation.projectID info:eu-repo/grantAgreement/ES/1PE/MTM2015-67304-P
• dc.rights Copyright for all articles in EJP is CC BY 4.0.
• dc.rights.accessRights info:eu-repo/semantics/openAccess
• dc.rights.uri https://creativecommons.org/licenses/by/4.0/
• dc.subject.keyword Regression functionalen
• dc.subject.keyword Nearest-neighbor-based estimateen
• dc.subject.keyword Asymptotic normalityen
• dc.subject.keyword Concentration inequalitiesen
• dc.subject.keyword Dimension reductionen
• dc.title A nearest neighbor estimate of the residual varianceen
• dc.type info:eu-repo/semantics/article
• dc.type.version info:eu-repo/semantics/publishedVersion