School of Mathematical Sciences

External Speaker: Antoine Usseglio-Carleve (INRIA Grenoble)

Location
Pharmacy A05
Date(s)
Thursday 28th March 2019 (14:00-15:00)
Contact
Gilles Stupfler
Description

Statistics and Probability seminar

Estimation of risk measures for conditioned elliptical distributions

This work focuses on the estimation of some risk measures for a real-valued random variable Y with a finite-dimensional covariate vector X. For that purpose, we will consider that the random vector (X,Y) is elliptically distributed. In a first time, we deal with the quantiles of Y given X = x. We thus firstly investigate a quantile regression model, widespread in the litterature, for which we get theoretical results. However, such a model has some limitations, especially when the quantile level is said to be extreme. Therefore, we propose another more suited approach. Asymptotic results are given, illustrated by a simulation study and a real data example. In a second chapter, we focus on another risk measure called expectile. The structure of the chapter is essentially the same as the previous one. Indeed, we first use a regression model that is not adapted to extreme expectiles, for which a methodological and statistical approach is proposed. Furthermore, highlighting the link between extreme quantiles and expectiles, we realize that other extreme risk measures are closely related to extreme quantiles. We will focus on two families called Lp-quantiles and Haezendonck-Goovaerts risk measures, for which we propose extreme estimators. A simulation study is also provided. Finally, the last chapter is devoted to the case where the size of the covariate vector X is large. By noticing that our previous estimators perform poorly in this case, we rely on some high dimensional estimation methods to propose other estimators. A simulation study gives a visual overview of their performances.

School of Mathematical Sciences

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