Padoan, Simone Stupfler, Gilles

Expectiles define a least squares analogue of quantiles. They have lately received substantial attention in actuarial and financial risk management contexts. Unlike quantiles, expectiles define coherent risk measures and are determined by tail expectations rather than tail probabilities; unlike the popular Expected Shortfall, they define elicitable...

Girard, Stéphane Stupfler, Gilles Usseglio-Carleve, Antoine

Expectiles define a least squares analogue of quantiles. They have been the focus of a substantial quantity of research in the context of actuarial and financial risk assessment over the last 10 years. Unlike quantiles, expectiles induce coherent risk measures and are calculated using tail expectations rather than merely tail probabilities ; contra...

Burdejová, Petra Härdle, Wolfgang K.
Published in
Computational Statistics

High-frequency data can provide us with a quantity of information for forecasting and help to calculate and prevent the future risk based on extremes. This tail behaviour is very often driven by exogenous components and may be modelled conditionally on other variables. However, many of these phenomena are observed over time, exhibiting non-trivial ...

Daouia, Abdelaati Girard, Stéphane Stupfler, Gilles

The class of quantiles lies at the heart of extreme-value theory and is one of the basic tools in risk management. The alternative family of expectiles is based on squared rather than absolute error loss minimization. It has recently been receiving a lot of attention in actuarial science, econometrics and statistical finance. Both quantiles and exp...

Bellini, Fabio Negri, Ilia Pyatkova, Mariya
Published in
Statistical Methods & Applications

Several statistical functionals such as quantiles and expectiles arise naturally as the minimizers of the expected value of a scoring function, a property that is called elicitability (see Gneiting in J Am Stat Assoc 106:746–762, 2011 and the references therein). The existence of such scoring functions gives a natural way to compare the accuracy of...

Usseglio-Carleve, Antoine

Cette thèse s'intéresse à l'estimation de certaines mesures de risque d'une variable aléatoire réelle Y en présence d'une covariable X. Pour cela, on va considérer que le vecteur (X,Y) suit une loi elliptique. Dans un premier temps, on va s'intéresser aux quantiles de Y sachant X=x. On va alors tester d'abord un modèle de régression quantile assez ...

Daouia, Abdelaati Girard, Stéphane Stupfler, Gilles

We use tail expectiles to estimate alternative measures to the Value at Risk (VaR) and Marginal Expected Shortfall (MES), two instruments of risk protection of utmost importance in actuarial science and statistical finance. The concept of expectiles isa least squares analogue of quantiles. Both are M-quanti les as the minimizers of an asymmetric co...

Diogo Barry, Amadou Charpentier, Arthur Oualkacha, Karim

Quantile and expectile regression models pertain to the estimation of unknown quantiles/expectiles of the cumulative distribution function of a dependent variable as a function of a set of covariates and a vector of regression coefficients. Both approaches make no assumption on the shape of the distribution of the response variable, allowing for in...

Schulze Waltrup, Linda Kauermann, Göran
Published in
Statistics and Computing

Expectile regression is a topic which became popular in the last years. It includes ordinary mean regression as special case but is more general as it offers the possibility to also model non-central parts of a distribution. Semi-parametric expectile models have recently been developed and it is easy to perform flexible expectile estimation with mo...

Coeurjolly, Jean-François Kortas, Hedi

In this paper, we introduce a new class of estimators of the Hurst exponent of the fractional Brownian motion (fBm) process. These estimators are based on sample expectiles of discrete variations of a sample path of the fBm process. In order to derive the statistical properties of the proposed estimators, we establish asymptotic results for sample ...