Joint inference on extreme expectiles for multivariate heavy-tailed distributions
@article{Padoan2020JointIO, title={Joint inference on extreme expectiles for multivariate heavy-tailed distributions}, author={Simone A. Padoan and Gilles Stupfler}, journal={Bernoulli}, year={2020} }
The notion of expectiles, originally introduced in the context of testing for homoscedasticity and conditional symmetry of the error distribution in linear regression, induces a law-invariant, coherent and elicitable risk measure that has received a significant amount of attention in actuarial and financial risk management contexts. A number of recent papers have focused on the behaviour and estimation of extreme expectile-based risk measures and their potential for risk management. Joint…
Figures and Tables from this paper
5 Citations
Extreme expectile estimation for short-tailed data
- Mathematics
- 2022
The use of expectiles in risk management contexts has recently gathered substantial momentum because of their excellent axiomatic and probabilistic properties. While expectile estimation at central…
Optimal pooling and distributed inference for the tail index and extreme quantiles
- Mathematics
- 2021
This paper investigates pooling strategies for tail index and extreme quantile estimation from heavy-tailed data. To fully exploit the information contained in several samples, we present general…
of the Bernoulli Society for Mathematical Statistics and Probability Volume Twenty Eight Number Two May 2022
- Mathematics
- 2020
A list of forthcoming papers can be found online at http://www.bernoullisociety.org/index. php/publications/bernoulli-journal/bernoulli-journal-papers CONTENTS 713 BELLEC, P.C. and ZHANG, C.-H.…
A review of probabilistic forecasting and prediction with machine learning
- Computer ScienceArXiv
- 2022
The topic of predictive uncertainty estimation with machine learning algorithms, as well as the related metrics (consistent scoring functions and proper scoring rules) for assessing probabilistic predictions are reviewed, sparking understanding on how to develop new algorithms tailored to users’ needs.
A modeler's guide to extreme value software
- Computer Science
- 2022
The intention, rather than to solely provide a catalog of existing software, is to discuss and compare existing implementations of statistical methods and to highlight numerical issues that are of practical importance yet are not typically discussed in theoretical or methodological papers.
References
SHOWING 1-10 OF 45 REFERENCES
Extreme expectile estimation for heavy-tailed time series
- Mathematics
- 2020
Expectiles are a least squares analogue of quantiles which have lately received substantial attention in actuarial and financial risk management contexts. Unlike quantiles, expectiles define coherent…
Estimation of tail risk based on extreme expectiles
- Economics, Mathematics
- 2016
We use tail expectiles to estimate alternative measures to the value at risk and marginal expected shortfall, which are two instruments of risk protection of utmost importance in actuarial science…
Tail expectile process and risk assessment
- MathematicsBernoulli
- 2020
Expectiles define a least squares analogue of quantiles. They are determined by tail expectations rather than tail probabilities. For this reason and many other theoretical and practical merits,…
Extreme M-quantiles as risk measures: From $L^{1}$ to $L^{p}$ optimization
- MathematicsBernoulli
- 2019
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…
Generalized Quantiles as Risk Measures
- Mathematics
- 2013
In the statistical and actuarial literature several generalizations of quantiles have been considered, by means of the minimization of a suitable asymmetric loss function. All these generalized…
Risk management with expectiles
- Mathematics
- 2014
Expectiles (EVaR) are a one-parameter family of coherent risk measures that have been recently suggested as an alternative to quantiles (VaR) and to expected shortfall (ES). In this work we review…
Estimation of the marginal expected shortfall: the mean when a related variable is extreme
- Mathematics, Economics
- 2012
Denote the loss return on the equity of a financial institution as X and that of the entire market as Y. For a given very small value of p>0, the marginal expected shortfall (MES) is defined as…
Of quantiles and expectiles: consistent scoring functions, Choquet representations and forecast rankings
- Mathematics
- 2015
In the practice of point prediction, it is desirable that forecasters receive a directive in the form of a statistical functional. For example, forecasters might be asked to report the mean or a…
Non‐parametric Estimation of Tail Dependence
- Mathematics, Computer Science
- 2006
This paper embeds tail dependence into the concept of tail copulae which describes the dependence structure in the tail of multivariate distributions but works more generally.