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We prove asymptotic normality of the so-called maximum likelihood estimator of the extreme value index.

- Laurens de Haan
- 2009

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)

- LAURENS DE HAAN, JOHN DE RONDE
- 1998

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)

- Jon Danielsson, Casper G. de Vries, Holger Drees, Laurens de Haan, Marc Henry
- 1997

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)

Tail index estimation depends for its accuracy on a precise choice of the sample fraction, i.e. the number of extreme order statistics on which the estimation is based. A complete solution to the sample fraction selection is given by means of a two step subsample bootstrap method. This method adaptively determines the sample fraction that minimizes the… (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)

- Paul Embre, Laurens de Haan, Xin Huang
- 1999

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)

- J. Geluk, L. de Haan, S. Resnick
- 1995

Second order regular variation is a reenement of the concept of regular variation which is useful for studying rates of convergence in extreme value theory and asymptotic normality of tail estimators. For a distribution tail 1 ? F which possesses second order regular variation, we discuss how this property is inherited by 1 ? F 2 and 1 ? F 2. We also… (More)