De Haan and Pereira (2006) [6] provided models for spatial extremes in the case of stationarity, which depend on just one parameter [beta]0 measuring tail dependence, and they proposed different estimators for this parameter. We supplement this framework by establishing local asymptotic...

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>

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...

The univariate piecing-together approach (PT) fits a univariate generalized Pareto distribution (GPD) to the upper tail of a given distribution function in a continuous manner. We propose a multivariate extension. First it is shown that an arbitrary copula is in the domain of attraction of a...

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...

Suppose that we are given an i.i.d. sample of size n from a distribution function F, which lies in a certain neigborhood of a generalized Pareto distribution. A suitable data transformation then reduces the estimation of extreme quantiles of F i.e., quantiles outside the range of our data, to...

Edgeworth expansions of length two are established for the sample quantile, preprivoted by a smoothed bootstrap, and for a studentized sample quantile, where we studentize by means of a kernel density estimate. As a consequence, it turns out that that two-sides confidence intervals for the...

Weak convergence is established for the maximum deviation of the bootstrap estimate of the sample q-quantile distribution.

Weak convergence of the remainder term in the Bahadur representation of the sample q-quantile is established, where q = qn tends to zero or one as the sample size n increases.