The existence and asymptotic properties of a backfitting projection algorithm under weak conditions

Oliver Linton, E. Mammen and J. Nielsen

LSE Research Online Documents on Economics from London School of Economics and Political Science, LSE Library

Abstract: We derive the asymptotic distribution of a new backfitting procedure for estimating the closest additive approximation to a nonparametric regression function. The procedure employs a recent projection interpretation of popular kernel estimators provided by Mammen, Marron, Turlach and Wand and the asymptotic theory of our estimators is derived using the theory of additive projections reviewed in Bickel, Klaassen, Ritov and Wellner. Our procedure achieves the same bias and variance as the oracle estimator based on knowing the other components, and in this sense improves on the method analyzed in Opsomer and Ruppert. We provide ‘‘high level’’ conditions independent of the sampling scheme. We then verify that these conditions are satisfied in a regression and a time series autoregression under weak conditions.

Keywords: Additive models; alternating projections; backfitting; kernel smoothing; local polynomials; nonparametric regression. AMS 1991 subject classifications : Primary 62G07; secondary 62G20. (search for similar items in EconPapers)
JEL-codes: C1 (search for similar items in EconPapers)
Date: 1999
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Citations: View citations in EconPapers (104)

Published in Annals of Statistics, 1999, 27(5), pp. 1443-1490. ISSN: 0090-5364

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Related works:
Working Paper: The Existence and Asymptotic Properties of a Backfitting Projection Algorithm under Weak Conditions (2000)
Working Paper: The existence and asymptotic properties of a backfitting projection algorithm under weak conditions (2000)
Working Paper: The Existence and Asymptotic Properties of a Backfitting Projection Algorithm Under Weak Conditions (1997)
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