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A Confidence Corridor for Expectile Functions

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  • Esra Akdeniz Duran
  • Mengmeng Guo
  • Wolfgang Karl Härdle

Abstract

Let (X1; Y1), ..., (Xn; Yn) be i.i.d. rvs and let v(x) be the unknown tau - 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 sup06x61 jvn(x)􀀀v(x)j. 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.

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Bibliographic Info

Paper provided by Sonderforschungsbereich 649, Humboldt University, Berlin, Germany in its series SFB 649 Discussion Papers with number SFB649DP2011-004.

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Length: 30 pages
Date of creation: Jan 2011
Date of revision:
Handle: RePEc:hum:wpaper:sfb649dp2011-004

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Related research

Keywords: Expectile Regression; Consistency Rate; Simultaneous confidence corridor; Asymmetric least squares; Kernel Smoothing;

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