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Local Nonlinear Least Squares Estimation: Using Parametric Information Nonparametrically

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Author Info
Pedro Gozalo (Brown University)
Oliver Linton (Cowles Foundation, Yale University)

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Abstract

We introduce a new kernel smoother for nonparametric regression that uses prior information on regression shape in the form of a parametric model. In effect, we nonparametrically encompass the parametric model. We derive pointwise and uniform consistency and the asymptotic distribution of our procedure. It has superior performance to the usual kernel estimators at or near the parametric model. It is particularly well motivated for binary data using the probit or logit parametric model as a base. We include an application to the Horowitz (1993) transport choice dataset.

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File URL: http://cowles.econ.yale.edu/P/cd/d10b/d1075.pdf
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Publisher Info
Paper provided by Cowles Foundation, Yale University in its series Cowles Foundation Discussion Papers with number 1075.

Download reference. The following formats are available: HTML (with abstract), plain text (with abstract), BibTeX, RIS (EndNote, RefMan, ProCite), ReDIF
Length: 41 pages
Date of creation: Aug 1994
Date of revision:
Handle: RePEc:cwl:cwldpp:1075

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Postal: Yale University, Box 208281, New Haven, CT 06520-8281 USA
Phone: (203) 432-3702
Fax: (203) 432-6167
Web page: http://cowles.econ.yale.edu/
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Postal: Cowles Foundation, Yale University, Box 208281, New Haven, CT 06520-8281 USA

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Related research
Keywords: Kernel; nonparametric regression; parametric regression; binary choice;

Find related papers by JEL classification:
C4 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: Special Topics
C5 - Mathematical and Quantitative Methods - - Econometric Modeling

References listed on IDEAS
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. Stoker, Thomas M, 1986. "Consistent Estimation of Scaled Coefficients," Econometrica, Econometric Society, vol. 54(6), pages 1461-81, November. [Downloadable!] (restricted)
  2. Gouriéroux, Christian & Monfort, Alain & Tenreiro, Carlos, 1994. "Kernel m-estimators : non parametric diagnostics for structural models," CEPREMAP Working Papers (Couverture Orange) 9405, CEPREMAP.
  3. Horowitz, Joel L., 1993. "Semiparametric estimation of a work-trip mode choice model," Journal of Econometrics, Elsevier, vol. 58(1-2), pages 49-70, July. [Downloadable!] (restricted)
  4. Herman Bierens & Hettie Pott-Buter, 1990. "Specification of household engel curves by nonparametric regression," Econometric Reviews, Taylor and Francis Journals, vol. 9(2), pages 123-184. [Downloadable!] (restricted)
  5. Manski, Charles F., 1975. "Maximum score estimation of the stochastic utility model of choice," Journal of Econometrics, Elsevier, vol. 3(3), pages 205-228, August. [Downloadable!] (restricted)
  6. Wolfgang Hardle & Oliver Linton, 1994. "Applied Nonparametric Methods," Cowles Foundation Discussion Papers 1069, Cowles Foundation, Yale University. [Downloadable!]
    Other versions:
  7. Horowitz, Joel L, 1992. "A Smoothed Maximum Score Estimator for the Binary Response Model," Econometrica, Econometric Society, vol. 60(3), pages 505-31, May. [Downloadable!] (restricted)
  8. Pakes, Ariel & Pollard, David, 1989. "Simulation and the Asymptotics of Optimization Estimators," Econometrica, Econometric Society, vol. 57(5), pages 1027-57, September. [Downloadable!] (restricted)
  9. Douglas A. McManus, 1994. "Making the Cobb-Douglas functional form an efficient nonparametric estimator through localization," Finance and Economics Discussion Series 94-31, Board of Governors of the Federal Reserve System (U.S.).
Full references

Cited by:
(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. Rosa Bernardini Papalia, 1999. "Local generalized method of moments estimation based on kernel weights: an application to panel data," Journal of Applied Statistics, Taylor and Francis Journals, vol. 26(8), pages 1005-1015, December. [Downloadable!] (restricted)
  2. Arthur Lewbel & Oliver Linton, 2003. "Nonparametric Estimation of Homothetic and Homothetically Separable Functions," STICERD - Econometrics Paper Series /2003/461, Suntory and Toyota International Centres for Economics and Related Disciplines, LSE. [Downloadable!]
    Other versions:
  3. Arthur Lewbel, 2004. "Estimation of Average Treatment Effects With Misclassification," Econometric Society 2004 North American Winter Meetings 210, Econometric Society. [Downloadable!]
    Other versions:
  4. Bossaerts, P. & Hillion, P., 1995. "Local Parametric Analysis of Hedging in Discrete Time," Discussion Paper 23, Tilburg University, Center for Economic Research. [Downloadable!]
    Other versions:
  5. Arthur Lewbel & Oliver Linton, 2003. "Nonparametric Matching and Efficient Estimators of Homothetically Separable Functions," Boston College Working Papers in Economics 585, Boston College Department of Economics, revised 04 Sep 2006. [Downloadable!]
    Other versions:
  6. Ron Mittelhammer & George Judge, 2008. "A Minimum Power Divergence Class of CDFs and Estimators for Binary Choice Models," Department of Agricultural & Resource Economics, UC Berkeley, Working Paper Series 1059, Department of Agricultural & Resource Economics, UC Berkeley. [Downloadable!]
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