IDEAS home Printed from https://ideas.repec.org/p/wpa/wuwpem/9608004.html
   My bibliography  Save this paper

Bootstrap Methods for Median Regression Models

Author

Listed:
  • 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
    Note: Zipped using PKZIP v2.04, encoded using UUENCODE v5.15. Zipped file includes 1 file --ui9609.wpa (TeX file 27 pages)
    as

    Download full text from publisher

    File URL: https://econwpa.ub.uni-muenchen.de/econ-wp/em/papers/9608/9608004.html
    Download Restriction: no

    File URL: https://econwpa.ub.uni-muenchen.de/econ-wp/em/papers/9608/9608004.pdf
    Download Restriction: no

    File URL: https://econwpa.ub.uni-muenchen.de/econ-wp/em/papers/9608/9608004.ps.gz
    Download Restriction: no
    ---><---

    Other versions of this item:

    References listed on IDEAS

    as
    1. repec:cup:etheor:v:11:y:1995:i:1:p:105-21 is not listed on IDEAS
    2. Powell, James L., 1984. "Least absolute deviations estimation for the censored regression model," Journal of Econometrics, Elsevier, vol. 25(3), pages 303-325, July.
    3. Koenker, Roger & Bassett, Gilbert, Jr, 1982. "Robust Tests for Heteroscedasticity Based on Regression Quantiles," Econometrica, Econometric Society, vol. 50(1), pages 43-61, January.
    4. 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.
    5. repec:cup:etheor:v:6:y:1990:i:2:p:123-50 is not listed on IDEAS
    6. 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.
    7. Pakes, Ariel & Pollard, David, 1989. "Simulation and the Asymptotics of Optimization Estimators," Econometrica, Econometric Society, vol. 57(5), pages 1027-1057, September.
    8. Koenker, Roger W & Bassett, Gilbert, Jr, 1978. "Regression Quantiles," Econometrica, Econometric Society, vol. 46(1), pages 33-50, January.
    9. Joel L. Horowitz, 1996. "Bootstrap Methods in Econometrics: Theory and Numerical Performance," Econometrics 9602009, University Library of Munich, Germany, revised 05 Mar 1996.
    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. Hahn, Jinyong, 1995. "Bootstrapping Quantile Regression Estimators," Econometric Theory, Cambridge University Press, vol. 11(1), pages 105-121, February.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Bilias, Yannis & Chen, Songnian & Ying, Zhiliang, 2000. "Simple resampling methods for censored regression quantiles," Journal of Econometrics, Elsevier, vol. 99(2), pages 373-386, December.
    2. Whang, Yoon-Jae, 2006. "Smoothed Empirical Likelihood Methods For Quantile Regression Models," Econometric Theory, Cambridge University Press, vol. 22(2), pages 173-205, April.
    3. Tae-Hwan Kim & Halbert White, 2003. "Estimation, Inference, And Specification Testing For Possibly Misspecified Quantile Regression," Advances in Econometrics, in: Maximum Likelihood Estimation of Misspecified Models: Twenty Years Later, pages 107-132, Emerald Group Publishing Limited.
    4. Honore, Bo & Khan, Shakeeb & Powell, James L., 2002. "Quantile regression under random censoring," Journal of Econometrics, Elsevier, vol. 109(1), pages 67-105, July.
    5. Parente, Paulo M.D.C. & Smith, Richard J., 2011. "Gel Methods For Nonsmooth Moment Indicators," Econometric Theory, Cambridge University Press, vol. 27(1), pages 74-113, February.
    6. Komunjer, Ivana, 2005. "Quasi-maximum likelihood estimation for conditional quantiles," Journal of Econometrics, Elsevier, vol. 128(1), pages 137-164, September.
    7. Moshe Buchinsky & Jinyong Hahn, 1998. "An Alternative Estimator for the Censored Quantile Regression Model," Econometrica, Econometric Society, vol. 66(3), pages 653-672, May.
    8. Chen, Songnian, 2018. "Sequential estimation of censored quantile regression models," Journal of Econometrics, Elsevier, vol. 207(1), pages 30-52.
    9. Peracchi, Franco, 2002. "On estimating conditional quantiles and distribution functions," Computational Statistics & Data Analysis, Elsevier, vol. 38(4), pages 433-447, February.
    10. Ichimura, Hidehiko & Todd, Petra E., 2007. "Implementing Nonparametric and Semiparametric Estimators," Handbook of Econometrics, in: J.J. Heckman & E.E. Leamer (ed.), Handbook of Econometrics, edition 1, volume 6, chapter 74, Elsevier.
    11. Gaglianone, Wagner Piazza & Lima, Luiz Renato & Linton, Oliver & Smith, Daniel R., 2011. "Evaluating Value-at-Risk Models via Quantile Regression," Journal of Business & Economic Statistics, American Statistical Association, vol. 29(1), pages 150-160.
    12. Moshe Buchinsky, 1998. "Recent Advances in Quantile Regression Models: A Practical Guideline for Empirical Research," Journal of Human Resources, University of Wisconsin Press, vol. 33(1), pages 88-126.
    13. Khan, Shakeeb, 2001. "Two-stage rank estimation of quantile index models," Journal of Econometrics, Elsevier, vol. 100(2), pages 319-355, February.
    14. William M. Rodgers, 2006. "Male White‐Black Wage Gaps, 1979‐1994: A Distributional Analysis," Southern Economic Journal, John Wiley & Sons, vol. 72(4), pages 773-793, April.
    15. Khan, Shakeeb & Powell, James L., 2001. "Two-step estimation of semiparametric censored regression models," Journal of Econometrics, Elsevier, vol. 103(1-2), pages 73-110, July.
    16. Halkos, George E., 2011. "Nonparametric modelling of biodiversity: Determinants of threatened species," Journal of Policy Modeling, Elsevier, vol. 33(4), pages 618-635, July.
    17. Elke Lüdemann & Ralf Wilke & Xuan Zhang, 2006. "Censored quantile regressions and the length of unemployment periods in West Germany," Empirical Economics, Springer, vol. 31(4), pages 1003-1024, November.
    18. Chernozhukov, Victor & Fernández-Val, Iván & Kowalski, Amanda E., 2015. "Quantile regression with censoring and endogeneity," Journal of Econometrics, Elsevier, vol. 186(1), pages 201-221.
    19. Hochgürtel, S., 1997. "Precautionary Motives and Portfolio Decisions," Other publications TiSEM a6aa05be-cbd8-4f92-ac8e-8, Tilburg University, School of Economics and Management.
    20. Michelle L. Barnes & Anthony W. Hughes, 2002. "A quantile regression analysis of the cross section of stock market returns," Working Papers 02-2, Federal Reserve Bank of Boston.

    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

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:wpa:wuwpem:9608004. See general information about how to correct material in RePEc.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: . General contact details of provider: https://econwpa.ub.uni-muenchen.de .

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: EconWPA (email available below). General contact details of provider: https://econwpa.ub.uni-muenchen.de .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service hosted by the Research Division of the Federal Reserve Bank of St. Louis . RePEc uses bibliographic data supplied by the respective publishers.