Heavy tailed phenomena are naturally analyzed by extreme value statistics. A crucial step in such an analysis is the estimation of the extreme value index, which describes the tail heaviness of the underlying probability distribution. We consider the situation where we have next to the n...

In this paper, we propose a test for the multivariate regular variation model. The test is based on testing whether the extreme value indices of the radial component conditional on the angular component falling in different subsets are the same. Combining the test on the constancy across...

A novel, general two-sample hypothesis testing procedure is established for testing the equality of tail copulas associated with bivariate data. More precisely, using an ingenious transformation of a natural two-sample tail copula process, a test process is constructed, which is shown to...

An omnibus test for spherical symmetry in R2 is proposed, employing localized empirical likelihood. The thus obtained test statistic is distribution-free under the null hypothesis. The asymptotic null distribution is established and critical values for typical sample sizes, as well as the...

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 MES...

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...

Let (X1, Y1), … , (Xn, Yn) be an i.i.d. sample from a bivariate distribution function that lies in the max-domain of attraction of an extreme value distribution. The asymptotic joint distribution of the standardized component-wise maxima max( Xi) and max(Yi) is then characterized by the...

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...

We extend classical extreme value theory to non-identically distributed observations. When the distribution tails are proportional much of extreme value statistics remains valid. The proportionality function for the tails can be estimated nonparametrically along with the (common) extreme value...

When simultaneously monitoring two possibly dependent, positive risks one is often interested in quantile regions with very small probability p. These extreme quantile regions contain hardly or no data and therefore statistical inference is difficult. In particular when we want to protect...