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SFB 649 Discussion Papers, HU Berlin >
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http://hdl.handle.net/10419/25269
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| Title: | | The stochastic fluctuation of the quantile regression curve  |
| 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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