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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

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Bibliographic Info

Paper provided by EconWPA in its series Econometrics with number 9608004.

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Length: 27 pages
Date of creation: 30 Aug 1996
Date of revision:
Handle: RePEc:wpa:wuwpem:9608004

Note: Zipped using PKZIP v2.04, encoded using UUENCODE v5.15. Zipped file includes 1 file --ui9609.wpa (TeX file 27 pages)
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  1. Hahn, Jinyong, 1995. "Bootstrapping Quantile Regression Estimators," Econometric Theory, Cambridge University Press, vol. 11(01), pages 105-121, February.
  2. Daniel Janas, 1993. "A smoothed bootstrap estimator for a studentized sample quantile," Annals of the Institute of Statistical Mathematics, Springer, vol. 45(2), pages 317-329, June.
  3. Koenker, Roger W & Bassett, Gilbert, Jr, 1978. "Regression Quantiles," Econometrica, Econometric Society, vol. 46(1), pages 33-50, January.
  4. 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.
  5. Koenker, Roger & Bassett, Gilbert, Jr, 1982. "Robust Tests for Heteroscedasticity Based on Regression Quantiles," Econometrica, Econometric Society, vol. 50(1), pages 43-61, January.
  6. Powell, James L., 1984. "Least absolute deviations estimation for the censored regression model," Journal of Econometrics, Elsevier, vol. 25(3), pages 303-325, July.
  7. Pakes, Ariel & Pollard, David, 1989. "Simulation and the Asymptotics of Optimization Estimators," Econometrica, Econometric Society, vol. 57(5), pages 1027-57, September.
  8. repec:cup:etheor:v:6:y:1990:i:2:p:123-50 is not listed on IDEAS
  9. Joel L. Horowitz, 1996. "Bootstrap Methods in Econometrics: Theory and Numerical Performance," Econometrics 9602009, EconWPA, revised 05 Mar 1996.
  10. Hall, Peter & Horowitz, Joel L., 1990. "Bandwidth Selection in Semiparametric Estimation of Censored Linear Regression Models," Econometric Theory, Cambridge University Press, vol. 6(02), pages 123-150, June.
  11. repec:cup:etheor:v:11:y:1995:i:1:p:105-21 is not listed on IDEAS
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