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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.

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Paper provided by London School of Economics and Political Science in its series Open Access publications from London School of Economics and Political Science with number http://eprints.lse.ac.uk/300/.

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Date of creation: 1999
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Publication status: Published in Annals of statistics (1999) v.27, p.1443-1490
Handle: RePEc:ner:lselon:http://eprints.lse.ac.uk/300/

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Find related papers by JEL classification:

• B12 - Schools of Economic Thought and Methodology - - History of Economic Thought through 1925 - - - Classical (includes Adam Smith)
• B31 - Schools of Economic Thought and Methodology - - History of Economic Thought: Individuals - - - Individuals
• D03 - Microeconomics - - General - - - Behavioral Economics; Underlying Principles

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1. Hardle, Wolfgang & Linton, Oliver, 1986. "Applied nonparametric methods," Handbook of Econometrics, in: R. F. Engle & D. McFadden (ed.), Handbook of Econometrics, edition 1, volume 4, chapter 38, pages 2295-2339 Elsevier.
   
   • Hardle, W., 1992. "Applied Nonparametric Methods," Papers 9204, Catholique de Louvain - Institut de statistique.
   • HÄRDLE, Wolfgang, 1992. "Applied nonparametric methods," CORE Discussion Papers 1992003, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
   • Oliver LINTON, . "Applied nonparametric methods," Statistic und Oekonometrie 9312, Humboldt Universitaet Berlin.
   • Wolfgang Hardle & Oliver Linton, 1994. "Applied Nonparametric Methods," Cowles Foundation Discussion Papers 1069, Cowles Foundation for Research in Economics, Yale University.
   • Hardle, W., 1992. "Applied Nonparametric Methods," Papers 9206, Tilburg - Center for Economic Research.
   • Hardle, W., 1992. "Applied Nonparametric Methods," Discussion Paper 1992-6, Tilburg University, Center for Economic Research.
2. Bollerslev, Tim & Engle, Robert F. & Nelson, Daniel B., 1986. "Arch models," Handbook of Econometrics, in: R. F. Engle & D. McFadden (ed.), Handbook of Econometrics, edition 1, volume 4, chapter 49, pages 2959-3038 Elsevier.
3. Masry, Elias, 1996. "Multivariate regression estimation local polynomial fitting for time series," Stochastic Processes and their Applications, Elsevier, vol. 65(1), pages 81-101, December.

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