Expectile Asymptotics

By Hajo Holzmann, Bernhard Klar. 2015

52 citations recorded by the source corpus.

We discuss in detail the asymptotic distribution of sample expectiles. First, we show uniform consistency under the assumption of a finite mean. In case of a finite second moment, we show that for expectiles other then the mean, only the additional assumption of continuity of the distribution function at the expectile implies asymptotic normality, otherwise, the limit is non-normal. For a continuous distribution function we show the uniform central limit theorem for the expectile process. If, in contrast, the distribution is heavy-tailed, and contained in the domain of attraction of a stable law with $1 < \alpha < 2$, then we show that the expectile is also asymptotically stable distributed. Our findings are illustrated in a simulation section.

Subfields: Economics and Econometrics, Finance

View Paper: https://www.semanticscholar.org/paper/d62e48d7e4be4cc8d69475f9210b437e468971d8

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In Economics and Econometrics

1. Irène Gijbels
2. Gilles Stupfler
3. Abdelaati Daouia
4. Léopold Simar
5. Paul Wilson

In Finance

1. Gilles Stupfler
2. Abdelaati Daouia
3. Irène Gijbels
4. Stéphane Girard

Citations in the corpus

• Extremiles: A New Perspective on Asymmetric Least Squares (2018, background): “According to de Haan and Ferreira (2006, Corollary 1.2.10), the model assumption F ∈ DA( γ ) is equivalent to the first-order regular variation condition: lim t→∞ q1−(tx)−1 q1−t−1 = xγ for all x > 0.”