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Confidence Bands In Quantile Regression

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  • Härdle, Wolfgang K.
  • Song, Song

Abstract

Let (X1, Y1), …, (Xn, Yn) be independent and identically distributed random variables and let l(x) be the unknown p-quantile regression curve of Y conditional on X. A quantile smoother ln(x) is a localized, 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, we consider the asymptotic maximal deviation sup0≤x≤1 |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 econometric model check. An economic application considers the relation between age and earnings in the labor market by means of parametric model specification tests, which presents a new framework to describe trends in the entire wage distribution in a parsimonious way.

Suggested Citation

  • Härdle, Wolfgang K. & Song, Song, 2010. "Confidence Bands In Quantile Regression," Econometric Theory, Cambridge University Press, vol. 26(4), pages 1180-1200, August.
    • Handle: RePEc:cup:etheor:v:26:y:2010:i:04:p:1180-1200_99
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    References listed on IDEAS

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