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Statistical Inference for Expectile‐based Risk Measures |
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| Authors: | Volker Krätschmer Henryk Zähle |
| Affiliation: | 1. Faculty of Mathematics, University of Duisburg‐Essen, Germany;2. Department of Mathematics, Saarland University, Germany |
| Abstract: | Expectiles were introduced by Newey and Powell in 1987 in the context of linear regression models. Recently, Bellini et al. revealed that expectiles can also be seen as reasonable law‐invariant risk measures. In this article, we show that the corresponding statistical functionals are continuous w.r.t. the 1‐weak topology and suitably functionally differentiable. By means of these regularity results, we can derive several properties such as consistency, asymptotic normality, bootstrap consistency and qualitative robustness of the corresponding estimators in nonparametric and parametric statistical models. |
| Keywords: | 1‐weak continuity asymptotic normality bootstrap consistency expectile‐based risk measure functional delta‐method qualitative robustness quasi‐Hadamard differentiability statistical estimation strong consistency weak dependence |