title: The Existence and Asymptotic Properties of a Backfitting Projection Algorithm under Weak Conditions
creator: Mammen, Enno
creator: Linton, Oliver
creator: Nielsen, Jens Perch
subject: 510
subject: 510 Mathematics
description: We derive the asymptotic distribution of a new backfitting procedure for estimating the closest additive approximation to a nonparametric regressionfunction. The procedure employs a recent projection interpretation ofpopular kernel estimators provided by Mammen et al. (1997), and theasymptotic theory of our estimators is derived using the theory of additiveprojections reviewed in Bickel et al. (1995). Our procedure achieves thesame bias and variance as the oracle estimator based on knowing the othercomponents, and in this sense improves on the method analyzed in Opsomer andRuppert (1997). We provide 'high level' conditions independent of thesampling scheme. We then verify that these conditions are satisfied in atime series autoregression under weak conditions.
date: 1998-05-08
type: Working paper
type: info:eu-repo/semantics/workingPaper
type: NonPeerReviewed
format: application/pdf
identifier: https://archiv.ub.uni-heidelberg.de/volltextserverhttps://archiv.ub.uni-heidelberg.de/volltextserver/20820/1/beitrag.46.pdf
identifier: DOI:10.11588/heidok.00020820
identifier: urn:nbn:de:bsz:16-heidok-208202
identifier:   Mammen, Enno ; Linton, Oliver ; Nielsen, Jens Perch  (1998) The Existence and Asymptotic Properties of a Backfitting Projection Algorithm under Weak Conditions.  [Working paper]     
relation: https://archiv.ub.uni-heidelberg.de/volltextserver/20820/
rights: info:eu-repo/semantics/openAccess
rights: http://archiv.ub.uni-heidelberg.de/volltextserver/help/license_urhg.html
language: eng