Abstract: Data depth measures the centrality of a point with respect to a given distribution or data cloud. It provides a natural center-outward ordering of multivariate data points and yields a systematic nonparametric multivariate analysis scheme. In particular, the halfspace depth is shown to...

Data depth measures the centrality of a point with respect to a given distribution or data cloud. It provides a natural center-outward ordering of multivariate data points and yields a systematic nonparametric multivariate analysis scheme. In particular, the halfspace depth is shown to have...

Consider the extreme quantile region, induced by the halfspace depth function HD, of the form Q = fx 2 Rd : HD(x; P) g, such that PQ = p for a given, very small p 0. This region can hardly be estimated through a fully nonparametric procedure since the sample halfspace depth is 0 outside the...

An elliptical copula model is a distribution function whose copula is that of an elliptical distri- bution. The tail dependence function in such a bivariate model has a parametric representation with two parameters: a tail parameter and a correlation parameter. The correlation parameter can be...

In this paper we maximize the efficiency of a multivariate S-estimator under a constraint on the breakdown point. In the linear regression model, it is known that the highest possible efficiency of a maximum breakdown S-estimator is bounded above by 33% for Gaussian errors. We prove the...

AMS classifications: 60G70; 62G32;

Tail dependence models for distributions attracted to a max-stable law are tted using observations above a high threshold. To cope with spatial, high-dimensional data, a rankbased M-estimator is proposed relying on bivariate margins only. A data-driven weight matrix is used to minimize the...

Consider a random sample in the max-domain of attraction of a multivariate extreme value distribution such that the dependence structure of the attractor belongs to a parametric model. A new estimator for the unknown parameter is defined as the value that minimises the distance between a vector...

Abstract: 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 E(X | Y QY (1−p)), where QY (1−p) is the (1−p)-th quantile of the distribution of Y...

The Half-Half (HH) plot is a new graphical method to investigate qualitatively the shape of a regression curve. The empirical HH-plot counts observations in the lower and upper quarter of a strip that moves horizontally over the scatter plot. The plot displays jumps clearly and reveals further...