Laurens de Haan

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Let Wi, i ∈ N, be independent copies of a zero-mean Gaussian process {W (t), t ∈ R d } with stationary increments and variance σ 2 (t). Independently of Wi, let ∞ i=1 δU i be a Poisson point process on the real line with intensity e −y dy. We show that the law of the random family of functions {Vi(·), i ∈ N}, where Vi(t) = Ui + Wi(t) − σ 2 (t)/2, is(More)
Multivariate extreme value theory is used to estimate the probability of failure of a sea-wall near the town of Petten in Noord Holland, The Netherlands. The sample consists of 828 observations of still water levels and wave heights collected during storm events over a 13-year period. The paper sketches the probabilistic and statistical theory behind the(More)
Economic problems such as large claims analysis in insurance and value-at-risk in finance , require assessment of the probability P of extreme realizations Q: This paper provides a semi-parametric method for estimation of extreme P ;Q combinations for data with heavy tails. We solve the long standing problem of estimating the sample threshold of where the(More)
APPENDIX For the relative compactness, we need several lemmas. First we present in Lemma 4.1 sufficient conditions for relative compactness; the proof is similar to that of Theorem 15.5 in Billingsley (1968), see also Neuhaus (1971). Lemma 4.1. Let P n be probability measures on (D 2 , L d). Suppose that, for each positive η, there exists an M > 0 such that(More)
An abundance of high quality data sets requiring heavy tailed models necessitates reliable methods of estimating the shape parameter governing the degree of tail heaviness. The Hill estimator is a popular method for doing this but its practical use is encumbered by several diiculties. We show that an alternative method of plotting Hill estimator values is(More)
For iid observations X 1 ; : : : ; Xn from a common distribution F with regularly varying tail 1?F(x) x ? L(x); x ! 1, the most popular estimator of is the Hill estimator. Regular variation of the distribution tail is equivalent to weak consistency of the Hill estimator in a manner made precise in Mason (1983) but necessary and suucient conditions for(More)
Rates of convergence of the distribution of the extreme order statistic to its limit distribution are given in the uniform metric and the total variation metric. A second{order regular variation condition is imposed by supposing a von Mises type condition which allows a uniied treatment. Rates are constructed from the parameters of the second{order regular(More)