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

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Author Info
Oliver Linton (Cowles Foundation, Yale University)
E. Mammen (Ruprecht-Karls-Universitat Heidelberg)
J. Nielsen (PFA Pension)

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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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Publisher Info
Paper provided by Cowles Foundation, 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:
Handle: RePEc:cwl:cwldpp:1160

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Postal: Cowles Foundation, Yale University, Box 208281, New Haven, CT 06520-8281 USA

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

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  1. J. Fan & W. H"Ardle & E. Mammen, . "Direct estimation of low dimensional components in additive models," Sonderforschungsbereich 373 1996-17, Humboldt Universitaet Berlin.
  2. J. P. Nielsen & O. B. Linton, . "An Optimization Interpretation of Integration and Backfitting Estimators for Separable Nonparametric Models," Sonderforschungsbereich 373 1996-88, Humboldt Universitaet Berlin.
  3. W. H"Ardle & O. Linton, . "Nonparametric Regression," Sonderforschungsbereich 373 1995-29, Humboldt Universitaet Berlin.
  4. L. Yang & W. Härdle & J. Nielsen, . "Nonparametric Autoregression with Multiplicative Volatility and Additive Mean," Sonderforschungsbereich 373 1998-107, Humboldt Universitaet Berlin.
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(explanations, Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.)

  1. Gao, Jiti & Lu, Zudi & Tjostheim, Dag, 2003. "Estimation in semiparametric spatial regression," MPRA Paper 11979, University Library of Munich, Germany, revised Jul 2005. [Downloadable!]
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  2. Oliver Linton & E. Mammen & J. Nielsen & C. Tanggaard, 1998. "Estimating Yield Curves by Kernel Smoothing Methods," Cowles Foundation Discussion Papers 1205, Cowles Foundation, Yale University. [Downloadable!]
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  3. Härdle, Wolfgang & Huet, Sylvie & Mammen, Enno & Sperlich, Stefan, 2001. "Bootstrap Inference in Semiparametric Generalized Additive Models," Finance Working Papers 01-3, University of Aarhus, Aarhus School of Business, Department of Business Studies. [Downloadable!]
  4. Oliver Linton & Enno Mammen, 2003. "Estimating Semiparametric ARCH (8) Models by Kernel Smoothing Methods," STICERD - Econometrics Paper Series /2003/453, Suntory and Toyota International Centres for Economics and Related Disciplines, LSE. [Downloadable!]
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  5. Gregory Connor & Matthias Hagmann & Oliver Linton, 2007. "Efficient Estimation of a SemiparametricCharacteristic-Based Factor Model of Security Returns," STICERD - Econometrics Paper Series /2007/524, Suntory and Toyota International Centres for Economics and Related Disciplines, LSE. [Downloadable!]
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  6. Oliver Linton & Yoon-Jae Whang, 2000. "Nonparametric Estimation with Aggregated Data," STICERD - Econometrics Paper Series /2000/397, Suntory and Toyota International Centres for Economics and Related Disciplines, LSE. [Downloadable!]
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  7. Woocheol Kim, 2004. "Identification And Estimation Of Nonparametric Structural," Econometric Society 2004 Far Eastern Meetings 733, Econometric Society. [Downloadable!]
  8. Oliver Linton & Enno Mammen & Jens Perch Nielsen & C Tanggaard, 2000. "Yield Curve Estimation by Kernel Smoothing Methods," STICERD - Econometrics Paper Series /2000/385, Suntory and Toyota International Centres for Economics and Related Disciplines, LSE. [Downloadable!]
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  9. Peroni, Chiara, 2007. "A non-parametric investigation of risk premia," MPRA Paper 5126, University Library of Munich, Germany, revised 01 Dec 2007. [Downloadable!]
  10. Wolfgang Haerdle & Oliver Linton & Qihua Wang, 2003. "Semiparametric Regression Analysis under Imputation for Missing Response Data," STICERD - Econometrics Paper Series /2003/454, Suntory and Toyota International Centres for Economics and Related Disciplines, LSE. [Downloadable!]
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  11. Rüdiger Krause & Gerhard Tutz, 2006. "Genetic algorithms for the selection of smoothing parameters in additive models," Computational Statistics, Springer, vol. 21(1), pages 9-31, March. [Downloadable!] (restricted)
  12. Azomahou, Theophile & Diene, Bity & Soete, Luc, 2009. "The role of consumption and the financing of health investment under epidemic shocks," UNU-MERIT Working Paper Series 006, United Nations University, Maastricht Economic and social Research and training centre on Innovation and Technology. [Downloadable!]
  13. Lijian Yang & Byeong U. Park & Lan Xue & Wolfgang Härdle, 2005. "Estimation and Testing for Varying Coefficients in Additive Models with Marginal Integration," SFB 649 Discussion Papers SFB649DP2005-047, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany. [Downloadable!]
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  14. Joel Horowitz & Enno Mammen, 2002. "Nonparametric estimation of an additive model with a link function," CeMMAP working papers CWP19/02, Centre for Microdata Methods and Practice, Institute for Fiscal Studies. [Downloadable!]
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  15. Stefan Profit & Stefan Sperlich, 2004. "Non-uniformity of job-matching in a transition economy - A nonparametric analysis for the Czech Republic," Applied Economics, Taylor and Francis Journals, vol. 36(7), pages 695-714, April. [Downloadable!] (restricted)
  16. Stefan Sperlich & Oliver Linton & Wolfgang Härdle, 1999. "Integration and backfitting methods in additive models-finite sample properties and comparison," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer, vol. 8(2), pages 419-458, December. [Downloadable!] (restricted)
  17. W. Kim & O. Linton, . "A Local Instrumental Estimation Method for Generalized Additive Volatility Models," Sonderforschungsbereich 373 2000-86, Humboldt Universitaet Berlin.
  18. Jing Wang & Lijian Yang, 2009. "Efficient and fast spline-backfitted kernel smoothing of additive models," Annals of the Institute of Statistical Mathematics, Springer, vol. 61(3), pages 663-690, September. [Downloadable!] (restricted)
  19. Woocheol Kim & Oliver Linton, 2003. "A Local Instrumental Variable Estimation Method for Generalized Additive Volatility Models," STICERD - Econometrics Paper Series /2003/456, Suntory and Toyota International Centres for Economics and Related Disciplines, LSE. [Downloadable!]
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  20. Oliver Linton & Jens Perch Nielsen & Sara van de Geer, 2001. "Estimating Multiplicative and Additive Hazard Functions by Kernel Methods," STICERD - Econometrics Paper Series /2001/411, Suntory and Toyota International Centres for Economics and Related Disciplines, LSE. [Downloadable!]
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