Resource title

The stochastic fluctuation of the quantile regression curve

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Resource description

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.

Resource author

Wolfgang Karl Härdle, Song Song

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Resource publish date

Resource language

eng

Resource content type

text/html

Resource resource URL

http://hdl.handle.net/10419/25269

Resource license

Adapt according to the presented license agreement and reference the original author.