Linton, Oliver, Mammen, E. and Nielsen, J. (1999) The existence and asymptotic properties of a backfitting projection algorithm under weak conditions. Annals of statistics, 27 (5). pp. 1443-1490. ISSN 0090-5364
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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.
| Item Type: | Article |
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| Official URL: | http://www.imstat.org/aos/ |
| Additional Information: | Published 1999 © Institute of Mathematical Statistics. LSE has developed LSE Research Online so that users may access research output of the School. Copyright © and Moral Rights for the papers on this site are retained by the individual authors and/or other copyright owners. Users may download and/or print one copy of any article(s) in LSE Research Online to facilitate their private study or for non-commercial research. You may not engage in further distribution of the material or use it for any profit-making activities or any commercial gain. You may freely distribute the URL (http://eprints.lse.ac.uk) of the LSE Research Online website. |
| Uncontrolled Keywords: | Additive models, alternating projections, backfitting, kernel smoothing, local polynomials, nonparametric regression. AMS 1991 subject classifications : Primary 62G07, secondary 62G20. |
| Library of Congress subject classification: | H Social Sciences > HA Statistics |
| Sets: | Research centres and groups > Financial Markets Group (FMG) Collections > Economists Online Research centres and groups > Suntory and Toyota International Centres for Economics and Related Disciplines (STICERD) Departments > Economics |
| Rights: | http://www.lse.ac.uk/library/rights/LSERO.htm |
| URL: | http://eprints.lse.ac.uk/300/ |
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