Annals of Statistics

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

E. Mammen, O. Linton, and J. Nielsen

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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.

Article information

Source
Ann. Statist., Volume 27, Number 5 (1999), 1443-1490.

Dates
First available in Project Euclid: 23 September 2004

Permanent link to this document
https://projecteuclid.org/euclid.aos/1017939138

Digital Object Identifier
doi:10.1214/aos/1017939138

Mathematical Reviews number (MathSciNet)
MR2001d:62040

Zentralblatt MATH identifier
0986.62028

Subjects
Primary: 62G07: Density estimation
Secondary: 62G20: Asymptotic properties

Keywords
Additive models alternating projections backfitting kernel smoothing local polynomials nonparametric regression

Citation

Mammen, E.; Linton, O.; Nielsen, J. The existence and asymptotic properties of a backfitting projection algorithm under weak conditions. Ann. Statist. 27 (1999), no. 5, 1443--1490. doi:10.1214/aos/1017939138. https://projecteuclid.org/euclid.aos/1017939138


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References

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  • GERMANY NEW HAVEN, CONNECTICUT 06520-8281 E-MAIL: mammen@statlab.uni-heidelberg.de E-MAIL: linton@econ.yale.edu

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