%0 Journal Article %1 WOS:000438839900052 %A Devroye, Luc %A Gyorfi, Laszlo %A Lugosi, Gabor %A Walk, Harro %C 3163 SOMERSET DR, CLEVELAND, OH 44122 USA %D 2018 %I INST MATHEMATICAL STATISTICS %J ELECTRONIC JOURNAL OF STATISTICS %K imported %N 1 %P 1752-1778 %R 10.1214/18-EJS1438 %T A nearest neighbor estimate of the residual variance %V 12 %X 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 is an element of R-d . 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.

@article{WOS:000438839900052, 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 is an element of R-d . 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.}, added-at = {2021-09-13T10:24:34.000+0200}, address = {3163 SOMERSET DR, CLEVELAND, OH 44122 USA}, affiliation = {Devroye, L (Corresponding Author), McGill Univ, Sch Comp Sci, 3480 Univ St, Montreal, PQ H3A 0E9, Canada. Devroye, Luc, McGill Univ, Sch Comp Sci, 3480 Univ St, Montreal, PQ H3A 0E9, Canada. Gyorfi, Laszlo, Budapest Univ Technol \& Econ, Dept Comp Sci \& Informat Theory, Magyar Tudosok Krt 2, H-1117 Budapest, Hungary. Lugosi, Gabor, Pompeu Fabra Univ, Dept Econ \& Business, Pg Llus Co 23, Barcelona 08010, Spain. Lugosi, Gabor, ICREA, Pg Llus Co 23, Barcelona 08010, Spain. Lugosi, Gabor, Barcelona Grad Sch Econ, Barcelona, Spain. Walk, Harro, Univ Stuttgart, Inst Stochast \& Anwendungen, Pfaffenwaldring 57, D-70569 Stuttgart, Germany.}, author = {Devroye, Luc and Gyorfi, Laszlo and Lugosi, Gabor and Walk, Harro}, author-email = {lucdevroye@gmail.com gyorfi@cs.bme.hu gabor.lugosi@upf.edu harro.walk@t-online.de}, biburl = {https://puma.ub.uni-stuttgart.de/bibtex/21d787ec0e700a243310945a760cebdc5/brittalenz}, da = {2021-08-10}, doc-delivery-number = {GN2PL}, doi = {10.1214/18-EJS1438}, funding-acknowledgement = {Natural Sciences and Engineering Research Council (NSERC) of CanadaNatural Sciences and Engineering Research Council of Canada (NSERC); National University of Public Service {[}KOFOP-2.1.2-VEKOP-15-2016-00001]; Spanish Ministry of Economy and Competitiveness {[}MTM2015-67304-P]; FEDER, EU}, funding-text = {Luc Devroye was supported by the Natural Sciences and Engineering Research Council (NSERC) of Canada.; Laszlo Gyorfi 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.; Gabor Lugosi was supported by the Spanish Ministry of Economy and Competitiveness, Grant MTM2015-67304-P and FEDER, EU.}, interhash = {34d1a9a1afda5e585125fae9e15c7d49}, intrahash = {1d787ec0e700a243310945a760cebdc5}, issn = {1935-7524}, journal = {ELECTRONIC JOURNAL OF STATISTICS}, journal-iso = {Electron. J. Stat.}, keywords = {imported}, language = {English}, number = 1, number-of-cited-references = {21}, oa = {gold, Green Published, Green Submitted}, pages = {1752-1778}, publisher = {INST MATHEMATICAL STATISTICS}, research-areas = {Mathematics}, times-cited = {3}, timestamp = {2021-09-13T08:26:47.000+0200}, title = {A nearest neighbor estimate of the residual variance}, type = {Article}, unique-id = {WOS:000438839900052}, usage-count-last-180-days = {0}, usage-count-since-2013 = {0}, volume = 12, web-of-science-categories = {Statistics \& Probability}, year = 2018 }