The stochastic fluctuation of the quantile regression curve - Wolfgang Karl Härdle; Song Song (Humboldt University of Berlin, Collaborative Research Center 649 - Economic Risk, 2008)
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: C00; C14; J01; J31; 330; Quantile Regression; Consistency Rate; Confidence Band; Check Function; Kernel Smoothing; Nonparametric Fitting; Regression; Statistischer Test; Stochastischer Prozess; Theorie; Schätzung; Lohn; Lebensalter; Arbeitsmarktdiskriminierung; USA