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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 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 < 1 but can be arbitrarily close to 1. In contrast, first-order asymptotic approximations make an error of size O(n-g). The bootstrap accounts for terms of size O(n-g) in the asymptotic expansions of the test statistics, whereas first-order approximations ignore these terms. These results also hold for symmetrical t and c2 tests for censored median regression models.

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

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

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Find related papers by JEL classification:
C1 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: General
C5 - Mathematical and Quantitative Methods - - Econometric Modeling
C8 - Mathematical and Quantitative Methods - - Data Collection and Data Estimation Methodology; Computer Programs

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. 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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(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!]
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  3. Yoon-Jae Whang, 2003. "Smoothed Empirical Likelihood Methods for Quantile Regression Models," Econometrics 0310005, EconWPA. [Downloadable!]
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  4. 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!]
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  5. 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!]
  6. 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!]
  7. 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!]
  8. Roger Koenker, 2000. "Inference on the Quantile Regression Process," Econometric Society World Congress 2000 Contributed Papers 0886, Econometric Society. [Downloadable!]
  9. 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:
  10. 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:
  11. 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!]
  12. Yang Yang & Tae-Hwy Lee, 2004. "Bagging Binary Predictors for Time Series," Econometric Society 2004 Far Eastern Meetings 512, Econometric Society. [Downloadable!]
  13. 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!]
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