We consider the extreme values of fractional Brownian motions, self-similar Gaussian processes and more general Gaussian processes which have a trend -ct[beta] for some constants c,[beta]0 and a variance t2H. We derive the tail behaviour of these extremes and show that they occur mainly in the...

It is known that the partial maximum of nonstationary Gaussian sequences converges in distribution and that the number of exceedances of a boundary is asymptotically a Poisson random variable, under certain restrictions. We investigate the rate of Poisson approximation for the number of...

We deal with the distribution of the first zero Rn of the real part of the empirical characteristic function related to a random variable X. Depending on the behaviour of the theoretical real part of the underlying characteristic function, several cases have to be considered. For most of the...

Any multivariate distribution can occur as the limit of extreme values in a sequence of independent, non-identically distributed random vectors. Under a reasonable uniform negligibility condition the class of such limit distribution can be totally characterized, which extends the known...

We consider general nonstationary max-autoregressive sequences Xi, i [greater-or-equal, slanted] 1, with Xi = Zimax(Xi - 1, Yi) where Yi, i [greater-or-equal, slanted] 1 is a sequence of i.i.d. random variables and Zi, i [greater-or-equal, slanted] 1 is a sequence of independent random variables...

In this paper multivariate extensions of the Friedman and Page tests for the comparison of several treatments are introduced. Related unadjusted and adjusted treatment effect estimates for the multivariate response variable are also found and their properties discussed. The test statistics and...

We analyse the asymptotic dependence structure of bivariate maxima in a triangular array of independent random vectors. This extends the analysis of the classical case of i.i.d. random vectors and the known relationship in the Gaussian case. We apply the general results to a special model and...

For i.i.d. bivariate normal vectors we consider the maxima of the projections with respect to two arbitrary directions. A limit theorem for these maxima is proved for the case that the angle of the two directions approaches zero. The result is generalized to a functional limit theorem.