The Stochastic Fluctuation of the Quantile Regression Curve

Wolfgang Karl Härdle and Song Song

No SFB649DP2008-027, SFB 649 Discussion Papers from Humboldt University, Collaborative Research Center 649

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.

Keywords: Quantile Regression; Consistency Rate; Confidence Band; Check Function; Kernel Smoothing; Nonparametric Fitting (search for similar items in EconPapers)
JEL-codes: C00 C14 J01 J31 (search for similar items in EconPapers)
New Economics Papers: this item is included in nep-ecm and nep-ore
Date: 2008-03
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