For estimating a rare event via the multivariate extreme value theory, the so-called tail dependence function has to be investigated (see [L. de Haan, J. de Ronde, Sea and wind: Multivariate extremes at work, Extremes 1 (1998) 7-45]). A simple, but effective estimator for the tail dependence...

We show consistency and asymptotic normality of certain estimators for expected exponential growth rates under i.i.d. observations. These statistical functionals are of the formT(F)=[integral operator]log[integral operator]h(x,y)F(dx)F(dy)and are applicable to dimension estimates (information...

We propose a multivariate method for combining results from independent studies about the same 'large scale' multiple testing problem. The method works asymptotically in the number of hypotheses and consists of applying the Benjamini-Hochberg procedure to the p-values of each study separately by...

The characteristic feature of operator selfsimilar stochastic processes is that a linear rescaling in time is equal in the sense of distributions to a linear operator rescaling in space, which in turn is characterized by the selfsimilarity exponent. The growth behaviour of such processes in any...

We derive the asymptotics of the OLS estimator for a purely autoregressive spatial model. Only low-level conditions are used. As the sample size increases, the spatial matrix is assumed to approach a square-integrable function on the square (0,1)2. The asymptotic distribution is a ratio of two...

Cross-periodograms can be used to study a multivariate spatial process observed on a lattice. For spatial data, it is often appropriate to study asymptotic properties of statistical procedures under fixed-domain asymptotics in which the number of observations increases in a fixed region while...

The joint distribution of X and N, where N has a geometric distribution and X is the sum of N IID exponential variables (independent of N), is infinitely divisible. This leads to a bivariate Lévy process {(X(t),N(t)),t=0}, whose coordinates are correlated negative binomial and gamma processes....

It is well-known that the univariate generalized Pareto distributions (GPD) are characterized by their peaks-over-threshold (POT) stability. We extend this result to multivariate GPDs. It is also shown that this POT stability is asymptotically shared by distributions which are in a certain...

If a one-sided test for a multivariate location parameter is inverted, the resulting confidence region may have an unpleasant shape. In particular, if the null and alternative hypothesis are both composite and complementary, the confidence region usually does not resemble the alternative...

Non-stationary time series arise in many settings, such as seismology, speech-processing, and finance. In many of these settings we are interested in points where a model of local stationarity is violated. We consider the problem of how to detect these change-points, which we identify by finding...