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The Stochastic Fluctuation of the Quantile Regression Curve

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  • Wolfgang Härdle
  • Song Song

Abstract

Let (X1, Y1), . . ., (Xn, Yn) be i.i.d. rvs and let l(x) be the unknown p-quantile regression curve of Y on X. A quantile-smoother ln(x) is a localised, nonlinear estimator of l(x). The strong uniform consistency rate is established under general conditions. In many applications it is necessary to know the stochastic fluctuation of the process {ln(x) - l(x)}. Using strong approximations of the empirical process and extreme value theory allows us to consider the asymptotic maximal deviation sup06x61 |ln(x)-l(x)|. The derived result helps in the construction of a uniform confidence band for the quantile curve l(x). This confidence band can be applied as a model check, e.g. in econometrics. An application considers a labour market discrimination effect.

Suggested Citation

  • Wolfgang Härdle & Song Song, 2008. "The Stochastic Fluctuation of the Quantile Regression Curve," SFB 649 Discussion Papers SFB649DP2008-027, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany.
    • Handle: RePEc:hum:wpaper:sfb649dp2008-027
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    File URL: http://sfb649.wiwi.hu-berlin.de/papers/pdf/SFB649DP2008-027.pdf
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    References listed on IDEAS

    as
    1. Cai, Zongwu, 2002. "Regression Quantiles For Time Series," Econometric Theory, Cambridge University Press, vol. 18(1), pages 169-192, February.
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    More about this item

    Keywords

    Quantile Regression; Consistency Rate; Confidence Band; Check Function; Kernel Smoothing; Nonparametric Fitting;
    All these keywords.

    JEL classification:

    • C00 - Mathematical and Quantitative Methods - - General - - - General
    • C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General
    • J01 - Labor and Demographic Economics - - General - - - Labor Economics: General
    • J31 - Labor and Demographic Economics - - Wages, Compensation, and Labor Costs - - - Wage Level and Structure; Wage Differentials

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