A confidence corridor for expectile functions - Esra Akdeniz Duran; Mengmeng Guo; Wolfgang Karl Härdle (Humboldt University of Berlin, Collaborative Research Center 649 - Economic Risk, 2010)
Let (X1, Y1), ..., (Xn, Yn) be i.i.d. rvs and let v(x) be the unknown T-expectile regression curve of Y conditional on X. An expectile-smoother vn(x) is a localized, nonlinear estimator of v(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 vn(x)-v(x). Using strong approximations of the empirical process and extreme value theory, we consider the asymptotic maximal deviation sup0<=x<=1 |vn(x)-v(x)|. The derived result helps in the construction of a uniform confidence band for the expectile curve v(x). This paper considers fitting a simultaneous confidence corridor (SCC)around the estimated expectile function of the conditional distribution of Y given x based on the observational data generated according to a nonparametric regression model. Moreover, we construct the simultaneous confidence corridors around the expectiles of the residuals from the temperature models to investigate the temperature risk drivers.
Keywords: C00; C14; J01; J31; 330; expectile regression; consistency rate; simultaneous confidence corridor; asymmetric least squares; kernel smoothing; Regression; Schätztheorie; Theorie