Conditional marginal expected shortfall

Yuri Goegebeur (1) , Armelle Guillou (2) , Nguyen Khanh Le Ho (1) , Jing Qin (1)

1 IMADA - Department of Mathematics and Computer Science [Odense]
2 IRMA - Institut de Recherche Mathématique Avancée

In the context of bivariate random variables (Y^{(1)}, Y^{(2)}), the marginal expected shortfall, defined as E(Y^{(1)} | Y^{(2)} \geq Q_2(1-p)) for p small, where Q_2 denotes the quantile function of Y^{(2)}, is an important risk measure, which finds applications in areas like, e.g., finance and environmental science. We consider estimation of the marginal expected shortfall when the random variables of main interest (Y^{(1)}, Y^{(2)}) are observed together with a random covariate X, leading to the concept of the conditional marginal expected shortfall. The asymptotic behavior of an estimator for this conditional marginal expected shortfall is studied for a wide class of conditional bivariate distributions, with heavy-tailed marginal conditional distributions, and where p tends to zero at an intermediate rate.

Mots clés: Marginal expected shortfall; empirical process; Pareto-type distribution; tail dependence

Domaines: Statistiques [math.ST]

Yuri Goegebeur, Armelle Guillou, Nguyen Khanh Le Ho, Jing Qin. Conditional marginal expected shortfall. 2019. ⟨hal-02272392v1⟩