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Bootstrap Critical Values for Tests Based on the Smoothed Maximum Score Estimator

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  • Joel L. Horowitz

    (Univ. of Iowa)

Abstract

The smoothed maximum score estimator of the coefficient vector of a binary response model is consistent and asymptotically normal under weak distributional assumptions. However, the differences between the true and nominal levels of tests based on smoothed maximum score estimates can be very large in finite samples when first- order asymptotics are used to obtain critical values. This paper shows that the bootstrap provides finite-sample critical values that are more accurate than those obtained from first-order asymptotic theory. In a set of Monte Carlo experiments carried out to check numerical performance, the bootstrap essentially eliminates large finite- sample distortions of level that occur when asymptotic critical values are used.

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Bibliographic Info

Paper provided by EconWPA in its series Econometrics with number 9603003.

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Length: 48 pages
Date of creation: 07 Mar 1996
Date of revision:
Handle: RePEc:wpa:wuwpem:9603003

Note: Zipped using PKZIP v2.04, encoded using UUENCODE v5.15. Zipped file includes 1 files -- ui9602.wpa (WordPerfect 5.0, 48 pages);
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References

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  1. Horowitz, Joel L, 1992. "A Smoothed Maximum Score Estimator for the Binary Response Model," Econometrica, Econometric Society, vol. 60(3), pages 505-31, May.
  2. Joel L. Horowitz, 1996. "Bootstrap Methods in Econometrics: Theory and Numerical Performance," Econometrics 9602009, EconWPA, revised 05 Mar 1996.
  3. J. L. HOROWITZ & Wolfgang HÄRDLE, 1994. "Direct Semiparametric Estimation of Single - Index Models with Discrete Covariates," SFB 373 Discussion Papers 1994,36, Humboldt University of Berlin, Interdisciplinary Research Project 373: Quantification and Simulation of Economic Processes.
  4. Han, Aaron K., 1987. "Non-parametric analysis of a generalized regression model : The maximum rank correlation estimator," Journal of Econometrics, Elsevier, vol. 35(2-3), pages 303-316, July.
  5. Powell, James L & Stock, James H & Stoker, Thomas M, 1989. "Semiparametric Estimation of Index Coefficients," Econometrica, Econometric Society, vol. 57(6), pages 1403-30, November.
  6. Sherman, Robert P, 1993. "The Limiting Distribution of the Maximum Rank Correlation Estimator," Econometrica, Econometric Society, vol. 61(1), pages 123-37, January.
  7. Cosslett, Stephen R, 1983. "Distribution-Free Maximum Likelihood Estimator of the Binary Choice Model," Econometrica, Econometric Society, vol. 51(3), pages 765-82, May.
  8. Horowitz, J.L., 1995. "Bootstrap Methods in Econometrics: Theory and Numerical Performance," Working Papers 95-10, University of Iowa, Department of Economics.
  9. Pakes, Ariel & Pollard, David, 1989. "Simulation and the Asymptotics of Optimization Estimators," Econometrica, Econometric Society, vol. 57(5), pages 1027-57, September.
  10. repec:wop:humbsf:1995-63 is not listed on IDEAS
  11. 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.
  12. J. L. Horowitz, 1995. "Bootstrap Methods In Econometrics: Theory And Numerical Performance," SFB 373 Discussion Papers 1995,63, Humboldt University of Berlin, Interdisciplinary Research Project 373: Quantification and Simulation of Economic Processes.
  13. 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.
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Citations

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Cited by:
  1. Bergström, Pål, 1999. "Bootstrap Methods and Applications in Econometrics - A Brief Survey," Working Paper Series 1999:2, Uppsala University, Department of Economics.
  2. Delgado, Miguel A. & Rodriguez-Poo, Juan M. & Wolf, Michael, 2001. "Subsampling inference in cube root asymptotics with an application to Manski's maximum score estimator," Economics Letters, Elsevier, vol. 73(2), pages 241-250, November.
  3. Abrevaya, Jason, 2000. "Rank estimation of a generalized fixed-effects regression model," Journal of Econometrics, Elsevier, vol. 95(1), pages 1-23, March.

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