报告题目 1: Simultaneous confidence bands for expectile functions

报告人：Prof. Dr. Wolfgang K. Haerdle 德国柏林洪堡大学 Ladislaus von Bortkiewicz 统计学讲席教授, 统计系主任

报告时间：2013年5月22日上午10点

报告地点：数学楼二楼学术报告厅

摘 要: Expectile regression, as a general M smoother, is used to capture the tail behaviour of a distribution. Let (X1,Y1), . . . , (Xn,Yn) be i.i.d. rvs. Denote by v(x) the unknown τ -expectile regression curve of Y conditional on X, and by vn(x) its kernel smoothing estimator. In this paper, we prove the strong uniform consistency rate of vn(x) under general conditions. Moreover, using strong approximations of the empirical process and extreme value theory, we consider the asymptotic maximal deviation sup0≤x≤1 |vn(x)−v(x)|. According to the asymptotic theory, we construct simultaneous confidence bands around the estimated expectile function. Furthermore,we apply this confidence band to temperature analysis. Taking Berlin and Taipei as an example, we investigate the temperature risk drivers to these two cities.