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 \mathbb E(Y^{(1)}|Y^{(2)} \ge 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. Our paper pioneers the statistical modeling of this risk measure 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. The finite sample performance is evaluated on a small simulation experiment. The practical applicability of the proposed estimator is illustrated on flood claim data.

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

Domaines: Statistiques [math.ST]

Yuri Goegebeur, Armelle Guillou, Nguyen Khanh Le Ho, Jing Qin. Conditional marginal expected shortfall. Extremes, 2021, 24, pp.797-847. ⟨10.1007/s10687-020-00403-1⟩. ⟨hal-02272392v4⟩