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Bootstrap Methods for Median Regression Models

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Author Info
Joel L. Horowitz

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Abstract

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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Publisher Info
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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References listed on IDEAS
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
  1. repec:cup:etheor:v:11:y:1995:i:1:p:105-21 is not listed on IDEAS
  2. Koenker, Roger & Bassett, Gilbert, Jr, 1982. "Robust Tests for Heteroscedasticity Based on Regression Quantiles," Econometrica, Econometric Society, vol. 50(1), pages 43-61, January. [Downloadable!] (restricted)
  3. Joel L. Horowitz, 1996. "Bootstrap Methods in Econometrics: Theory and Numerical Performance," Econometrics 9602009, EconWPA, revised 05 Mar 1996. [Downloadable!]
  4. Koenker, Roger W & Bassett, Gilbert, Jr, 1978. "Regression Quantiles," Econometrica, Econometric Society, vol. 46(1), pages 33-50, January. [Downloadable!] (restricted)
  5. 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. [Downloadable!]
  6. 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. [Downloadable!] (restricted)
  7. Koenker Roger, 1982. "Robust methods in econometrics," Econometric Reviews, Taylor and Francis Journals, vol. 1(2), pages 213-255. [Downloadable!] (restricted)
  8. repec:cup:etheor:v:6:y:1990:i:2:p:123-50 is not listed on IDEAS
  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. [Downloadable!] (restricted)
  10. Hahn, Jinyong, 1995. "Bootstrapping Quantile Regression Estimators," Econometric Theory, Cambridge University Press, vol. 11(01), pages 105-121, February. [Downloadable!]
  11. Pakes, Ariel & Pollard, David, 1989. "Simulation and the Asymptotics of Optimization Estimators," Econometrica, Econometric Society, vol. 57(5), pages 1027-57, September. [Downloadable!] (restricted)
  12. Powell, James L., 1984. "Least absolute deviations estimation for the censored regression model," Journal of Econometrics, Elsevier, vol. 25(3), pages 303-325, July. [Downloadable!] (restricted)
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Cited by:
(explanations, Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.)

  1. Yoshihiko Nishiyama & Peter M Robinson, 2005. "The Bootstrap and the Edgeworth Correction for Semiparametric Averaged Derivatives," STICERD - Econometrics Paper Series /2005/483, Suntory and Toyota International Centres for Economics and Related Disciplines, LSE. [Downloadable!]
  2. Hidehiko Ichimura & Sokbae Lee, 2006. "Characterization of the Asymptotic Distribution of Semiparametric M-Estimators," CIRJE F-Series CIRJE-F-426, CIRJE, Faculty of Economics, University of Tokyo. [Downloadable!]
    Other versions:
  3. Olivier Armantier & Amadou Boly, 2008. "Can Corruption Be Studied in the Lab? Comparing a Field and a Lab Experiment," CIRANO Working Papers 2008s-26, CIRANO. [Downloadable!]
  4. Roger Koenker, 2000. "Inference on the Quantile Regression Process," Econometric Society World Congress 2000 Contributed Papers 0886, Econometric Society. [Downloadable!]
  5. Xiaohong Chen & Oliver Linton & Ingrid Van Keilegom, 2003. "Estimation of Semiparametric Models when the Criterion Function is not Smooth," STICERD - Econometrics Paper Series /2003/450, Suntory and Toyota International Centres for Economics and Related Disciplines, LSE. [Downloadable!]
    Other versions:
  6. Yoon-Jae Whang, 2004. "Smoothed Empirical Likelihood Methods for Quantile Regression Models," Cowles Foundation Discussion Papers 1453, Cowles Foundation, Yale University. [Downloadable!]
    Other versions:
  7. Halbert White & Tae-Hwan Kim, 2002. "Estimation, Inference, and Specification Testing for Possibly Misspecified Quantile Regression," University of California at San Diego, Economics Working Paper Series 2002-09, Department of Economics, UC San Diego. [Downloadable!]
  8. Gong, Xiaodong & van Soest, Arthur & Zhang, Ping, 2000. "Sexual Bias and Household Consumption: A Semiparametric Analysis of Engel Curves in Rural China," IZA Discussion Papers 212, Institute for the Study of Labor (IZA). [Downloadable!]
    Other versions:
  9. Paulo Parente & Richard Smith, 2008. "GEL methods for non-smooth moment indicators," CeMMAP working papers CWP19/08, Centre for Microdata Methods and Practice, Institute for Fiscal Studies. [Downloadable!]
  10. Juan Carlos Escanciano & Carlos Velasco, 2008. "Specification Tests of Parametric Dynamic Conditional Quantiles," Caepr Working Papers 2008-021, Center for Applied Economics and Policy Research, Economics Department, Indiana University Bloomington. [Downloadable!]
  11. Y. Nishiyama & Peter Robinson, 2004. "The bootstrap and the Edgeworth correction for semiparametric averaged derivatives," CeMMAP working papers CWP12/04, Centre for Microdata Methods and Practice, Institute for Fiscal Studies. [Downloadable!]
    Other versions:
  12. George Anastassopoulos & Fragkiskos Filippaios & Paul Phillips, 2007. "An ‘eclectic’ investigation of tourism multinationals’ activities: Evidence from the Hotels and Hospitality Sector in Greece," GreeSE – Hellenic Observatory Papers on Greece and Southeast Europe 08, Hellenic Observatory, LSE. [Downloadable!]
  13. Yang Yang & Tae-Hwy Lee, 2004. "Bagging Binary Predictors for Time Series," Econometric Society 2004 Far Eastern Meetings 512, Econometric Society. [Downloadable!]
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