The existence and asymptotic properties of a backfitting projection algorithm under weak conditions
AbstractWe 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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Bibliographic InfoPaper 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/.
Date of creation: 1999
Date of revision:
Publication status: Published in Annals of statistics (1999) v.27, p.1443-1490
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Other versions of this item:
- Oliver Linton & E. Mammen & J. Nielsen, 1997. "The Existence and Asymptotic Properties of a Backfitting Projection Algorithm Under Weak Conditions," Cowles Foundation Discussion Papers 1160, Cowles Foundation for Research in Economics, Yale University.
- Oliver Linton & Enno Mammen & N Nielsen, 2000. "The Existence and Asymptotic Properties of a Backfitting Projection Algorithm under Weak Conditions," STICERD - Econometrics Paper Series /2000/386, Suntory and Toyota International Centres for Economics and Related Disciplines, LSE.
- 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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