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Improving The Efficiency And Robustness Of The Smoothed Maximum Score Estimator

  • Francisco Alvarez-Cuadrado

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    The binary-response maximum score (MS) estimator is a robust estimator, which can accommodate heteroskedasticity of an unknown form; J. Horowitz (1992) defined a smoothed maximum score estimator SMS) and demonstrated that this improves the convergence rate for sufficiently smooth conditional error densities. In this paper we relax Horowitz’s smoothness assumptions of the model and extend his asymptotic results. We also derive a joint limiting distribution of estimators with different bandwidths and smoothing kernels. We construct an estimator that combines SMS estimators for different bandwidths and kernels to overcome the uncertainty over choice of bandwidth when the degree of smoothnes of error distribution is unknown. A Monte Carlo study demonstrates the gains in efficiency and robustness.

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    File URL: http://www.mcgill.ca/files/economics/msdec21.pdf
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    Paper provided by McGill University, Department of Economics in its series Departmental Working Papers with number 2004-01.

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    Length: 34 pages
    Date of creation: Sep 2006
    Date of revision:
    Handle: RePEc:mcl:mclwop:2004-01
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    1. Horowitz, Joel L., 2002. "Bootstrap critical values for tests based on the smoothed maximum score estimator," Journal of Econometrics, Elsevier, vol. 111(2), pages 141-167, December.
    2. Horowitz, Joel L, 1992. "A Smoothed Maximum Score Estimator for the Binary Response Model," Econometrica, Econometric Society, vol. 60(3), pages 505-31, May.
    3. Arthur Lewbel, 1999. "Semiparametric Qualitative Response Model Estimation with Unknown Heteroskedasticity or Instrumental Variables," Boston College Working Papers in Economics 454, Boston College Department of Economics.
    4. 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.
    5. Zinde-Walsh, Victoria, 2002. "Asymptotic Theory For Some High Breakdown Point Estimators," Econometric Theory, Cambridge University Press, vol. 18(05), pages 1172-1196, October.
    6. Manski, Charles F. & Thompson, T. Scott, 1986. "Operational characteristics of maximum score estimation," Journal of Econometrics, Elsevier, vol. 32(1), pages 85-108, June.
    7. Manski, Charles F., 1985. "Semiparametric analysis of discrete response : Asymptotic properties of the maximum score estimator," Journal of Econometrics, Elsevier, vol. 27(3), pages 313-333, March.
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