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Local Nonlinear Least Squares Estimation: Using Parametric Information Nonparametrically

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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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Bibliographic Info

Paper provided by Cowles Foundation for Research in Economics, Yale University in its series Cowles Foundation Discussion Papers with number 1075.

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Length: 41 pages
Date of creation: Aug 1994
Date of revision:
Handle: RePEc:cwl:cwldpp:1075

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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: Kernel; nonparametric regression; parametric regression; binary choice;

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References

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  1. Wolfgang Hardle & Oliver Linton, 1994. "Applied Nonparametric Methods," Cowles Foundation Discussion Papers 1069, Cowles Foundation for Research in Economics, Yale University.
  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.
  4. Pakes, Ariel & Pollard, David, 1989. "Simulation and the Asymptotics of Optimization Estimators," Econometrica, Econometric Society, vol. 57(5), pages 1027-57, September.
  5. Horowitz, Joel L, 1992. "A Smoothed Maximum Score Estimator for the Binary Response Model," Econometrica, Econometric Society, vol. 60(3), pages 505-31, May.
  6. Fenton, Victor M & Gallant, A Ronald, 1996. "Convergence Rates of SNP Density Estimators," Econometrica, Econometric Society, vol. 64(3), pages 719-27, May.
  7. 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.
  8. 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.).
  9. 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.
  10. Stoker, Thomas M, 1986. "Consistent Estimation of Scaled Coefficients," Econometrica, Econometric Society, vol. 54(6), pages 1461-81, November.
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Citations

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Cited by:
  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 & Francis Journals, vol. 26(8), pages 1005-1015.
  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.
  3. Arthur Lewbel, 2004. "Estimation of Average Treatment Effects With Misclassification," Econometric Society 2004 North American Winter Meetings 210, Econometric Society.
  4. Arthur Lewbel & Oliver Linton, 2007. "Nonparametric Matching and Efficient Estimators of Homothetically Separable Functions," Econometrica, Econometric Society, vol. 75(4), pages 1209-1227, 07.
  5. Mittelhammer, Ron C. & Judge, George, 2011. "A family of empirical likelihood functions and estimators for the binary response model," Journal of Econometrics, Elsevier, vol. 164(2), pages 207-217, October.
  6. Mittelhammer, Ron C Dr. & Judge, George G., 2008. "A Minimum Power Divergence Class of CDFs and Estimators for Binary Choice Models," Department of Agricultural & Resource Economics, UC Berkeley, Working Paper Series qt7bc2828q, Department of Agricultural & Resource Economics, UC Berkeley.
  7. Bossaerts, Peter & Hillion, Pierre, 1997. "Local parametric analysis of hedging in discrete time," Journal of Econometrics, Elsevier, vol. 81(1), pages 243-272, November.
  8. Gozalo, Pedro L., 1997. "Nonparametric bootstrap analysis with applications to demographic effects in demand functions," Journal of Econometrics, Elsevier, vol. 81(2), pages 357-393, December.

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