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The second-order bias of quantile estimators

Author

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  • 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
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    References listed on IDEAS

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    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, January.
    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, Decembrie.
    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.
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    Cited by:

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    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.

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    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

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