We investigate the sojourn time above a high threshold of a continuous stochastic process Y=(Yt)t∈[0,1]. It turns out that the limit, as the threshold increases, of the expected sojourn time given that it is positive, exists if the copula process corresponding to Y is in the functional domain...

We consider a random vector <Emphasis Type="BoldItalic">X, whose components are neither necessarily independent nor identically distributed. The fragility index (FI), if it exists, is defined as the limit of the expected number of exceedances among the components of <Emphasis Type="BoldItalic">X above a high threshold, given that there is at least...</emphasis></emphasis>

This paper deals with the estimation of dependence parameters in certain bivariate generalized Pareto models which are models for exceedances (peaks) over high thresholds. A unified approach is obtained by using canonical parameters. An estimator, which is related to a best linear unbiased...

It is shown that the accuracy of the bootstrap estimate of the quantile function pertaining to the distribution of the sample q-quantile based on n independent and identically distributed observations is exactly Op(l/n), q [epsilon] (0, 1) fixed. Thi improved considerably by applying smoothed...

A distribution function (df) F is said to belong to the p-max domain of attraction of a nondegenerate df G, iff there exist [alpha]n 0, [beta]n 0 such that the df Fn([alpha]n x [beta]n sign(x)) converges weakly to G. The class of possible limiting dfs G and their domains of attraction are...

It is well known that the sample covariance is not an efficient estimator of the covariance of a bivariate normal vector. We extend this result to elliptical distributions and we propose a simple explicit estimator, which is efficient in the normal case and which outperforms the sample...

The comedianCOM(X, Y) of random variablesX,Yis a median based robust alternative to the covariance ofXofY. For the bivariate normal case it is known thatCOM(X, Y), standardized by the median absolute deviations ofXandY, is a symmetric, strictly increasing and continuous function of the...