IDEAS home Printed from https://ideas.repec.org/a/eee/ecolet/v173y2018icp143-147.html
   My bibliography  Save this article

The second-order bias of quantile estimators

Author

Listed:
  • Lee, Tae-Hwy
  • Ullah, Aman
  • Wang, He

Abstract

The finite sample theory using higher-order asymptotics provides better approximations of the bias for a class of estimators. Phillips (1991) demonstrated the higher-order asymptotic expansions for LAD estimators. Rilstone et al. (1996) provided the second-order bias results of conditional mean regression estimators. This paper develops new analytical results on the second-order bias of the conditional quantile regression estimators, which enables an improved bias correction and thus to obtain improved quantile estimation. In particular, we show that the second-order bias is larger towards the tails of the conditional density than near the median, and therefore the benefit of the second-order bias correction is greater when we are interested in the deeper tail quantiles, e.g., for the study of income distribution and financial risk management. The Monte Carlo simulation confirms the theory that the bias is larger at the tail quantiles, and the second-order bias correction improves the behavior of the quantile estimators.

Suggested Citation

  • Lee, Tae-Hwy & Ullah, Aman & Wang, He, 2018. "The second-order bias of quantile estimators," Economics Letters, Elsevier, vol. 173(C), pages 143-147.
    • Handle: RePEc:eee:ecolet:v:173:y:2018:i:c:p:143-147
    DOI: 10.1016/j.econlet.2018.09.022
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0165176518303999
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.econlet.2018.09.022?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Komunjer, Ivana, 2005. "Quasi-maximum likelihood estimation for conditional quantiles," Journal of Econometrics, Elsevier, vol. 128(1), pages 137-164, September.
    2. Joel L. Horowitz, 1998. "Bootstrap Methods for Median Regression Models," Econometrica, Econometric Society, vol. 66(6), pages 1327-1352, November.
    3. Bao, Yong & Ullah, Aman, 2007. "The second-order bias and mean squared error of estimators in time-series models," Journal of Econometrics, Elsevier, vol. 140(2), pages 650-669, October.
    4. Graham Elliott & Allan Timmermann & Ivana Komunjer, 2005. "Estimation and Testing of Forecast Rationality under Flexible Loss," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 72(4), pages 1107-1125.
    5. Koenker,Roger, 2005. "Quantile Regression," Cambridge Books, Cambridge University Press, number 9780521845731.
    6. Rilstone, Paul & Srivastava, V. K. & Ullah, Aman, 1996. "The second-order bias and mean squared error of nonlinear estimators," Journal of Econometrics, Elsevier, vol. 75(2), pages 369-395, December.
    7. Ullah, Aman, 2004. "Finite Sample Econometrics," OUP Catalogue, Oxford University Press, number 9780198774488.
    8. Koenker, Roger W & Bassett, Gilbert, Jr, 1978. "Regression Quantiles," Econometrica, Econometric Society, vol. 46(1), pages 33-50, January.
    9. Joshua Angrist & Victor Chernozhukov & Iván Fernández-Val, 2006. "Quantile Regression under Misspecification, with an Application to the U.S. Wage Structure," Econometrica, Econometric Society, vol. 74(2), pages 539-563, March.
    10. Phillips, P.C.B., 1991. "A Shortcut to LAD Estimator Asymptotics," Econometric Theory, Cambridge University Press, vol. 7(4), pages 450-463, December.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Yong Bao & Aman Ullah, 2021. "Analytical Finite Sample Econometrics: From A. L. Nagar to Now," Journal of Quantitative Economics, Springer;The Indian Econometric Society (TIES), vol. 19(1), pages 17-37, December.
    2. Katal, Ali & Mortezazadeh, Mohammad & Wang, Liangzhu (Leon), 2019. "Modeling building resilience against extreme weather by integrated CityFFD and CityBEM simulations," Applied Energy, Elsevier, vol. 250(C), pages 1402-1417.

    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. Tae-Hwy Lee & Aman Ullah & He Wang, 2023. "The Second-order Bias and Mean Squared Error of Quantile Regression Estimators," Working Papers 202313, University of California at Riverside, Department of Economics.
    2. Tae-Hwy Lee & Aman Ullah & He Wang, 2024. "The second-order bias and mean squared error of quantile regression estimators," Indian Economic Review, Springer, vol. 59(1), pages 11-68, October.
    3. Galvao, Antonio F. & Kato, Kengo, 2016. "Smoothed quantile regression for panel data," Journal of Econometrics, Elsevier, vol. 193(1), pages 92-112.
    4. Komunjer, Ivana, 2013. "Quantile Prediction," Handbook of Economic Forecasting, in: G. Elliott & C. Granger & A. Timmermann (ed.), Handbook of Economic Forecasting, edition 1, volume 2, chapter 0, pages 961-994, Elsevier.
    5. Escanciano, J.C. & Goh, S.C., 2014. "Specification analysis of linear quantile models," Journal of Econometrics, Elsevier, vol. 178(P3), pages 495-507.
    6. Gneiting, Tilmann, 2011. "Quantiles as optimal point forecasts," International Journal of Forecasting, Elsevier, vol. 27(2), pages 197-207, April.
    7. repec:hal:journl:peer-00732534 is not listed on IDEAS
    8. Grigory Franguridi & Bulat Gafarov & Kaspar Wüthrich, 2021. "Conditional Quantile Estimators: A Small Sample Theory," CESifo Working Paper Series 9046, CESifo.
    9. Otsu, Taisuke, 2008. "Conditional empirical likelihood estimation and inference for quantile regression models," Journal of Econometrics, Elsevier, vol. 142(1), pages 508-538, January.
    10. Gneiting, Tilmann, 2011. "Quantiles as optimal point forecasts," International Journal of Forecasting, Elsevier, vol. 27(2), pages 197-207.
    11. Escanciano, Juan Carlos & Velasco, Carlos, 2010. "Specification tests of parametric dynamic conditional quantiles," Journal of Econometrics, Elsevier, vol. 159(1), pages 209-221, November.
    12. Escanciano, Juan Carlos & Velasco, Carlos, 2010. "Specification tests of parametric dynamic conditional quantiles," Journal of Econometrics, Elsevier, vol. 159(1), pages 209-221, November.
    13. Cai, Zongwu & Chen, Linna & Fang, Ying, 2018. "A semiparametric quantile panel data model with an application to estimating the growth effect of FDI," Journal of Econometrics, Elsevier, vol. 206(2), pages 531-553.
    14. Kengo Kato, 2012. "Asymptotic normality of Powell’s kernel estimator," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 64(2), pages 255-273, April.
    15. Fan, Yanqin & Liu, Ruixuan, 2016. "A direct approach to inference in nonparametric and semiparametric quantile models," Journal of Econometrics, Elsevier, vol. 191(1), pages 196-216.
    16. Chesher, Andrew, 2017. "Understanding the effect of measurement error on quantile regressions," Journal of Econometrics, Elsevier, vol. 200(2), pages 223-237.
    17. 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.
    18. Yu, Jun, 2012. "Bias in the estimation of the mean reversion parameter in continuous time models," Journal of Econometrics, Elsevier, vol. 169(1), pages 114-122.
    19. Chen, Xirong & Li, Degui & Li, Qi & Li, Zheng, 2019. "Nonparametric estimation of conditional quantile functions in the presence of irrelevant covariates," Journal of Econometrics, Elsevier, vol. 212(2), pages 433-450.
    20. Wiji Arulampalam & Alison Booth & Mark Bryan, 2010. "Are there asymmetries in the effects of training on the conditional male wage distribution?," Journal of Population Economics, Springer;European Society for Population Economics, vol. 23(1), pages 251-272, January.
    21. Graham, Bryan S. & Hahn, Jinyong & Poirier, Alexandre & Powell, James L., 2018. "A quantile correlated random coefficients panel data model," Journal of Econometrics, Elsevier, vol. 206(2), pages 305-335.

    More about this item

    Keywords

    Delta function; Quantile regression; Second-order bias;
    All these keywords.

    JEL classification:

    • C1 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General
    • C2 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables
    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General

    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:eee:ecolet:v:173:y:2018:i:c:p:143-147. See general information about how to correct material in RePEc.

    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: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/locate/ecolet .

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

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.