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Bootstrap Methods for Median Regression Models

  • Joel L. Horowitz

The least-absolute-deviations (LAD) estimator for a median-regression or censored 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. The smoothed estimator is asymptotically equivalent to the ordinary LAD estimator. With bootstrap critical values, the rejection probabilities of symmetrical t and chi-square tests based on the smoothed estimator are correct to nearly order 1/n under the null hypothesis. In contrast, first-order asymptotic approximations make errors of this size.

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Article provided by Econometric Society in its journal Econometrica.

Volume (Year): 66 (1998)
Issue (Month): 6 (November)
Pages: 1327-1352

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Handle: RePEc:ecm:emetrp:v:66:y:1998:i:6:p:1327-1352
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  1. Joel L. Horowitz, 1996. "Bootstrap Methods in Econometrics: Theory and Numerical Performance," Econometrics 9602009, EconWPA, revised 05 Mar 1996.
  2. Hahn, Jinyong, 1995. "Bootstrapping Quantile Regression Estimators," Econometric Theory, Cambridge University Press, vol. 11(01), pages 105-121, February.
  3. repec:cup:etheor:v:11:y:1995:i:1:p:105-21 is not listed on IDEAS
  4. repec:cup:etheor:v:6:y:1990:i:2:p:123-50 is not listed on IDEAS
  5. Koenker, Roger W & Bassett, Gilbert, Jr, 1978. "Regression Quantiles," Econometrica, Econometric Society, vol. 46(1), pages 33-50, 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. 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.
  9. 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.
  10. 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.
  11. Koenker, Roger & Bassett, Gilbert, Jr, 1982. "Robust Tests for Heteroscedasticity Based on Regression Quantiles," Econometrica, Econometric Society, vol. 50(1), pages 43-61, January.
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