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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)

- Laurens de Haan
- 2009

Let Wi, i ∈ N, be independent copies of a zero-mean Gaussian process {W (t), t∈ R} with stationary increments and variance σ(t). Independently of Wi, let ∑∞ i=1 δUi be a Poisson point process on the real line with intensity e dy. We show that the law of the random family of functions {Vi(·), i ∈N}, where Vi(t) = Ui +Wi(t)− σ (t)/2, is translation invariant.… (More)

Received November 2002; revised June 2003. Supported by Netherlands Organization for Scientific Research through the Netherlands Mathematical Research Foundation and by the Heisenberg program of the DFG. Supported in part by POCTI/FCT/FEDER. AMS 2000 subject classifications. Primary 62G32; secondary 62G20.

The main goal of this paper is to develop, under a semi-parametric context, asymptotically normal estimators of the second order parameter ρ, a parameter related to the rate of convergence of maximum values, linearly normalized, towards its limit. Asymptotic normality of such estimators is achieved under a third order condition on the tail 1 − F of the… (More)

- C. G. DE VRIES, Harry Garretsen, +4 authors Stefan Straetmans
- 2004

Banks are linked through the interbank deposit market, participations like syndicated loans and deposit interest rate risk. The similarity in exposures carries the potential for systemic breakdowns. This potential is either weak or strong, depending on whether the linkages remain or vanish asymptotically. It is shown that the linearity of the bank… (More)

Consider n i.i.d. random vectors on R, with unknown, common distribution function F . Under a sharpening of the extreme value condition on F , we derive a weighted approximation of the corresponding tail copula process. Then we construct a test to check whether the extreme value condition holds by comparing two estimators of the limiting extreme value… (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)

- 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)

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

- Laurens de Haan
- 1995

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)