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Statistical Inference for Expectile‐based Risk Measures
Author(s) -
Krätschmer Volker,
Zähle Henryk
Publication year - 2017
Publication title -
scandinavian journal of statistics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.359
H-Index - 65
eISSN - 1467-9469
pISSN - 0303-6898
DOI - 10.1111/sjos.12259
Subject(s) - mathematics , estimator , statistical inference , nonparametric statistics , asymptotic distribution , strong consistency , differentiable function , parametric statistics , consistency (knowledge bases) , inference , econometrics , robustness (evolution) , weak consistency , nonparametric regression , statistics , discrete mathematics , pure mathematics , artificial intelligence , computer science , biochemistry , chemistry , gene
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.