Related papers: Set-valued expectiles for ordered data analysis

Set-valued quantiles for multivariate distributions with respect to a general convex cone are introduced which are based on a family of (univariate) distribution functions rather than on the joint distribution function. It is shown that…

The use of expectiles in risk management has recently gathered remarkable momentum due to their excellent axiomatic and probabilistic properties. In particular, the class of elicitable law-invariant coherent risk measures only consists of…

Algorithms are proposed for the computation of set-valued quantiles and the values of the lower cone distribution function for bivariate data sets. These new objects make data analysis possible involving an order relation for the data…

Many key quantities in statistics and probability theory such as the expectation, quantiles, expectiles and many risk measures are law-determined maps from a space of random variables to the reals. We call such a law-determined map, which…

Sublinear functionals of random variables are known as sublinear expectations; they are convex homogeneous functionals on infinite-dimensional linear spaces. We extend this concept for set-valued functionals defined on measurable set-valued…

The present article is devoted to the semi-parametric estimation of multivariate expectiles for extreme levels. The considered multivariate risk measures also include the possible conditioning with respect to a functional covariate,…

Expectiles are statistical parameters which also provide a class of sublinear risk measures in finance. They are solutions of continuous optimization problems. The corresponding first order condition provides two different fixed point…

A generalization of expectiles for d-dimensional multivariate distribution functions is introduced. The resulting geometric expectiles are unique solutions to a convex risk minimization problem and are given by d-dimensional vectors. They…

We introduce a new class of multivariate heavy-tailed distributions that are convolutions of heterogeneous multivariate t-distributions. Unlike commonly used heavy-tailed distributions, the multivariate convolution-t distributions embody…

The concept of univariate Range Value-at-Risk, presented by Cont et al. (2010), is extended in the multidimensional setting. Traditional risk measures are not well suited when dealing with heavy-tail distributions and infinite tail…

Cone distribution functions from statistics are turned into Multi-Criteria Decision Making tools. It is demonstrated that this procedure can be considered as an upgrade of the weighted sum scalarization insofar as it absorbs a whole…

Expectiles were introduced by Newey and Powell (1987) in the context of linear regression models. Recently, Bellini et al. (2014) revealed that expectiles can also be seen as reasonable law-invariant risk measures. In this article, we show…

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…

To provide a comprehensive summary of the tail distribution, the expected shortfall is defined as the average over the tail above (or below) a certain quantile of the distribution. The expected shortfall regression captures the…

Despite the renewed interest in the Newey and Powell (1987) concept of expectiles in fields such as econometrics, risk management, and extreme value theory, expectile regression---or, more generally, M-quantile regression---unfortunately…

Conformal prediction is a powerful framework for distribution-free uncertainty quantification. The standard approach to conformal prediction relies on comparing the ranks of prediction scores: under exchangeability, the rank of a future…

This paper features expectiles in dynamic and stochastic optimization. Expectiles are a family of risk functionals characterized as minimizers of optimization problems. For this reason, they enjoy various unique stability properties, which…

Quantiles, expectiles and extremiles can be seen as concepts defined via an optimization problem, where this optimization problem is driven by two important ingredients: the loss function as well as a distributional weight function. This…

Expectile, as the minimizer of an asymmetric quadratic loss function, is a coherent risk measure and is helpful to use more information about the distribution of the considered risk. In this paper, we propose a new risk measure by replacing…

This paper is devoted to the introduction and study of a new family of multivariate elicitable risk measures. We call the obtained vector-valued measures multivariate expectiles. We present the different approaches used to construct our…