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The Existence and Asymptotic Properties of a Backfitting Projection Algorithm Under Weak Conditions

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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 et al. (1997), and the asymptotic theory of our estimators is derived using the theory of additive projections reviewed in Bickel et al. (1995). 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 (1997). We provide 'high level' conditions independent of the sampling scheme. We then verify that these conditions are satisfied in a time series autoregression under weak conditions.

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File URL: http://cowles.econ.yale.edu/P/cd/d11b/d1160.pdf
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Bibliographic Info

Paper provided by Cowles Foundation for Research in Economics, Yale University in its series Cowles Foundation Discussion Papers with number 1160.

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Length: 39 pages
Date of creation: Sep 1997
Date of revision:
Publication status: Published in The Annals of Statistics (1999), 27: 1443-1490
Handle: RePEc:cwl:cwldpp:1160

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Web page: http://cowles.econ.yale.edu/
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Postal: Cowles Foundation, Yale University, Box 208281, New Haven, CT 06520-8281 USA

Related research

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

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  1. Yang, Lijian & Härdle, Wolfgang & Nielsen, Jens P., 1998. "Nonparametric autoregression with multiplicative volatility and additive mean," SFB 373 Discussion Papers 1998,107, Humboldt University of Berlin, Interdisciplinary Research Project 373: Quantification and Simulation of Economic Processes.
  2. HÄRDLE, Wolfgang, 1992. "Applied nonparametric methods," CORE Discussion Papers 1992003, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
  3. Oliver LINTON, . "Applied nonparametric methods," Statistic und Oekonometrie 9312, Humboldt Universitaet Berlin.
  4. 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.
  5. J. FAN & Wolfgang HÄRDLE & Enno MAMMEN, 1996. "Direct estimation of low dimensional components in additive models," SFB 373 Discussion Papers 1996,17, Humboldt University of Berlin, Interdisciplinary Research Project 373: Quantification and Simulation of Economic Processes.
  6. 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.
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