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Estimation of semiparametric models when the criterion function is not smooth

  • Xiaohong Chen

    ()

    (Institute for Fiscal Studies and Yale University)

  • Oliver Linton

    ()

    (Institute for Fiscal Studies and University of Cambridge)

  • Ingred van Keilegom

    (Institute for Fiscal Studies)

We provide easy to verify suffcient conditions for the consistency and asymptotic normality of a class of semiparametric optimization estimators where the criterion function does not obey standard smoothness conditions and simultaneously depends on some preliminary nonparametric estimators. Our results extend existing theories like those of Pakes and Pollard (1989), Andrews (1994a), and Newey (1994). We apply our results to two examples: a 'hit rate' and a partially linear median regression with some endogenous regressors.

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File URL: http://cemmap.ifs.org.uk/wps/cwp0202.pdf
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Paper provided by Centre for Microdata Methods and Practice, Institute for Fiscal Studies in its series CeMMAP working papers with number CWP02/02.

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Length: 28 pp.
Date of creation: 07 Nov 2002
Date of revision:
Handle: RePEc:ifs:cemmap:02/02
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  1. Arthur Lewbel & Oliver Linton, 2000. "Nonparametric Censored and Truncated Regression," Boston College Working Papers in Economics 439, Boston College Department of Economics.
  2. Joel L. Horowitz, 1998. "Bootstrap Methods for Median Regression Models," Econometrica, Econometric Society, vol. 66(6), pages 1327-1352, November.
  3. Richard W. Blundell & Martin Browning & Ian A. Crawford, 2003. "Nonparametric Engel Curves and Revealed Preference," Econometrica, Econometric Society, vol. 71(1), pages 205-240, January.
  4. Newey, Whitney K. & McFadden, Daniel, 1986. "Large sample estimation and hypothesis testing," Handbook of Econometrics, in: R. F. Engle & D. McFadden (ed.), Handbook of Econometrics, edition 1, volume 4, chapter 36, pages 2111-2245 Elsevier.
  5. O. B. LINTON & R. CHEN & Wolfgang HÄRDLE, 1995. "An Analysis of Transformations for Additive Nonparanetric Regression," SFB 373 Discussion Papers 1995,68, Humboldt University of Berlin, Interdisciplinary Research Project 373: Quantification and Simulation of Economic Processes.
  6. Newey, W.K., 1991. "The Asymptotic Variance of Semiparametric Estimators," Working papers 583, Massachusetts Institute of Technology (MIT), Department of Economics.
  7. Donald J. Brown & Marten H. Wegkamp, 2001. "Weighted Minimum Mean-Square Distance from Independence Estimation," Cowles Foundation Discussion Papers 1288, Cowles Foundation for Research in Economics, Yale University.
  8. Xiaohong Chen & Xiaotong Shen, 1998. "Sieve Extremum Estimates for Weakly Dependent Data," Econometrica, Econometric Society, vol. 66(2), pages 289-314, March.
  9. Robinson, Peter M, 1988. "Root- N-Consistent Semiparametric Regression," Econometrica, Econometric Society, vol. 56(4), pages 931-54, July.
  10. Hall, Peter & Horowitz, Joel L, 1996. "Bootstrap Critical Values for Tests Based on Generalized-Method-of-Moments Estimators," Econometrica, Econometric Society, vol. 64(4), pages 891-916, July.
  11. Horowitz, Joel L, 1992. "A Smoothed Maximum Score Estimator for the Binary Response Model," Econometrica, Econometric Society, vol. 60(3), pages 505-31, May.
  12. Andrews, Donald W.K., 1995. "Nonparametric Kernel Estimation for Semiparametric Models," Econometric Theory, Cambridge University Press, vol. 11(03), pages 560-586, June.
  13. Ariel Pakes & Steven Olley, 1994. "A Limit Theorem for a Smooth Class of Semiparametric Estimators," Cowles Foundation Discussion Papers 1066, Cowles Foundation for Research in Economics, Yale University.
  14. repec:cup:etheor:v:11:y:1995:i:3:p:560-96 is not listed on IDEAS
  15. Chen, Songnian & Khan, Shakeeb, 2001. "Semiparametric Estimation Of A Partially Linear Censored Regression Model," Econometric Theory, Cambridge University Press, vol. 17(03), pages 567-590, June.
  16. Powell, James L., 1984. "Least absolute deviations estimation for the censored regression model," Journal of Econometrics, Elsevier, vol. 25(3), pages 303-325, July.
  17. 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.
  18. Pakes, Ariel & Pollard, David, 1989. "Simulation and the Asymptotics of Optimization Estimators," Econometrica, Econometric Society, vol. 57(5), pages 1027-57, September.
  19. Manski, Charles F, 1983. "Closest Empirical Distribution Estimation," Econometrica, Econometric Society, vol. 51(2), pages 305-19, March.
  20. Andrews, Donald W K, 1994. "Asymptotics for Semiparametric Econometric Models via Stochastic Equicontinuity," Econometrica, Econometric Society, vol. 62(1), pages 43-72, January.
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