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The Existence and Asymptotic Properties of a Backfitting Projection Algorithm under Weak Conditions

Mammen, Enno ; Linton, Oliver ; Nielsen, Jens Perch

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Abstract

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.

Item Type: Working paper
Place of Publication: Heidelberg
Date Deposited: 02 Jun 2016 07:14
Date: 8 May 1998
Number of Pages: 39
Faculties / Institutes: The Faculty of Mathematics and Computer Science > Department of Applied Mathematics
Subjects: 510 Mathematics
Uncontrolled Keywords: Additive models, Alternating projections, Backfitting, Kernel Smoothing, Local Polynomials, Nonparametric Regression
Schriftenreihe ID: Beiträge zur Statistik > Beiträge
Additional Information: Abweichender Titel: Backfitting under weak conditions
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