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Simultaneous confidence bands for expectile functions

Mengmeng Guo () and Wolfgang Härdle ()

AStA Advances in Statistical Analysis, 2012, vol. 96, issue 4, 517-541

Abstract: Expectile regression, as a general M smoother, is used to capture the tail behaviour of a distribution. Let (X 1 ,Y 1 ),…,(X n ,Y n ) be i.i.d. rvs. Denote by v(x) the unknown τ-expectile regression curve of Y conditional on X, and by v n (x) its kernel smoothing estimator. In this paper, we prove the strong uniform consistency rate of v n (x) under general conditions. Moreover, using strong approximations of the empirical process and extreme value theory, we consider the asymptotic maximal deviation sup 0≤x≤1 |v n (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. Copyright Springer-Verlag 2012

Keywords: Expectile regression; Consistency rate; Simultaneous confidence bands; Asymmetric least squares; Kernel smoothing (search for similar items in EconPapers)
Date: 2012
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DOI: 10.1007/s10182-011-0182-1

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