Internet auctions attract numerous agents, but only a few become active bidders. A major difficulty in the structural analysis of internet auctions is that the number of potential bidders is unknown. Under the independent private value paradigm (IPVP)the valuations of the active bidders form a...

The selection of upper order statistics in tail estimation is notoriously difficult. Methods that are based on asymptotic arguments, like minimizing the asymptotic MSE, do not perform well in finite samples. Here, we advance a data-driven method that minimizes the maximum distance between 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 selection of upper order statistics in tail estimation is notoriously difficult. Most methods are based on asymptotic arguments, like minimizing the asymptotic mse, that do not perform well in finite samples. Here we advance a data driven method that minimizes the maximum distance between...

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...

The statistical theory of extremes is extended to observations that are non-stationary and not independent. The non-stationarity over time and space is controlled via the scedasis (tail scale) in the marginal distributions. Spatial dependence stems from multivariate extreme value theory. We...

There is no scientific consensus on the fundamental question whether the probability distribution of the human life span has a finite endpoint or not and, if so, whether this upper limit changes over time. Our study uses a unique dataset of the ages at death - in days - of all (about 285,000)...

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...

Let X1,X2,... be i.i.d. random variables and let their distribution be in the domain of attraction of an extreme value distribution. Quite a few estimators of the extreme value index are known to be consistent under the domain of attraction conditions. When it comes to asymptotic normality a...

Recently, a weighted approximation for the tail empirical distribution function has been developed (Approximations to the tail empirical distribution function with application to testing extreme value conditions. preprint, submitted for publication). We show that the same result can also be used...