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October 1999 The existence and asymptotic properties of a backfitting projection algorithm under weak conditions
E. Mammen, O. Linton, J. Nielsen
Ann. Statist. 27(5): 1443-1490 (October 1999). DOI: 10.1214/aos/1017939138

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.

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E. Mammen. O. Linton. J. Nielsen. "The existence and asymptotic properties of a backfitting projection algorithm under weak conditions." Ann. Statist. 27 (5) 1443 - 1490, October 1999. https://doi.org/10.1214/aos/1017939138

Information

Published: October 1999
First available in Project Euclid: 23 September 2004

zbMATH: 0986.62028
MathSciNet: MR2001D:62040
Digital Object Identifier: 10.1214/aos/1017939138

Subjects:
Primary: 62G07
Secondary: 62G20

Rights: Copyright © 1999 Institute of Mathematical Statistics

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Vol.27 • No. 5 • October 1999
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