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Title:The stochastic fluctuation of the quantile regression curve PDF Logo
Authors:Härdle, Wolfgang Karl
Song, Song
Issue Date:2008
Series/Report no.:SFB 649 discussion paper 2008,027
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 n(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.
Subjects:Quantile Regression , Consistency Rate , Confidence Band , Check Function , Kernel Smoothing , Nonparametric Fitting
JEL:C00
C14
J01
J31
Document Type:Working Paper
Appears in Collections:SFB 649 Discussion Papers, HU Berlin

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