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

Oliver Linton, Enno Mammen and N Nielsen

STICERD - Econometrics Paper Series from Suntory and Toyota International Centres for Economics and Related Disciplines, LSE

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 (1997), and the asymptotic theory of our estimators is derived using the theory of additive projections reviewed in Bickel, Klaassen, Ritov, and Wellner (1993). 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 analysed in Opsomer and Ruppert (1997). 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. (search for similar items in EconPapers)
Date: 2000-04
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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 (1999)
Working Paper: The Existence and Asymptotic Properties of a Backfitting Projection Algorithm Under Weak Conditions (1997)
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Persistent link: https://EconPapers.repec.org/RePEc:cep:stiecm:386

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