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Bootstrap Methods for Median Regression Models

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  • Joel L. Horowitz

Abstract

The least-absolute-deviations (LAD) estimator for a median-regression model does not satisfy the standard conditions for obtaining asymptotic refinements through use of the bootstrap because the LAD objective function is not smooth. This paper overcomes this problem by smoothing the objective function so that it becomes differentiable. The smoothed estimator is asymptotically equivalent to the standard LAD estimator. With bootstrap critical values, the levels of symmetrical t and c2 tests based on the smoothed estimator are correct through O(n-g), where g

Suggested Citation

  • Joel L. Horowitz, 1996. "Bootstrap Methods for Median Regression Models," Econometrics 9608004, University Library of Munich, Germany.
  • Handle: RePEc:wpa:wuwpem:9608004
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    References listed on IDEAS

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    1. repec:cup:etheor:v:11:y:1995:i:1:p:105-21 is not listed on IDEAS
    2. Daniel Janas, 1993. "A smoothed bootstrap estimator for a studentized sample quantile," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 45(2), pages 317-329, June.
    3. Pakes, Ariel & Pollard, David, 1989. "Simulation and the Asymptotics of Optimization Estimators," Econometrica, Econometric Society, vol. 57(5), pages 1027-1057, September.
    4. Powell, James L., 1984. "Least absolute deviations estimation for the censored regression model," Journal of Econometrics, Elsevier, vol. 25(3), pages 303-325, July.
    5. Koenker, Roger W & Bassett, Gilbert, Jr, 1978. "Regression Quantiles," Econometrica, Econometric Society, vol. 46(1), pages 33-50, January.
    6. Koenker, Roger & Bassett, Gilbert, Jr, 1982. "Robust Tests for Heteroscedasticity Based on Regression Quantiles," Econometrica, Econometric Society, vol. 50(1), pages 43-61, January.
    7. Joel L. Horowitz, 1996. "Bootstrap Methods in Econometrics: Theory and Numerical Performance," Econometrics 9602009, University Library of Munich, Germany, revised 05 Mar 1996.
    8. Hall, Peter & Horowitz, Joel L., 1990. "Bandwidth Selection in Semiparametric Estimation of Censored Linear Regression Models," Econometric Theory, Cambridge University Press, vol. 6(2), pages 123-150, June.
    9. Buchinsky, Moshe, 1995. "Estimating the asymptotic covariance matrix for quantile regression models a Monte Carlo study," Journal of Econometrics, Elsevier, vol. 68(2), pages 303-338, August.
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    11. repec:cup:etheor:v:6:y:1990:i:2:p:123-50 is not listed on IDEAS
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    More about this item

    JEL classification:

    • C1 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General
    • C5 - Mathematical and Quantitative Methods - - Econometric Modeling
    • C8 - Mathematical and Quantitative Methods - - Data Collection and Data Estimation Methodology; Computer Programs

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