http://repub.eur.nl/res/aut/1897/ List of Publications en http://repub.eur.nl/static-eur/img/logo.png http://repub.eur.nl http://repub.eur.nl/res/pub/15234/ 2008-12-01T00:00:00Z We study the Kolmogorov-Smirnov test, Berk-Jones test, score test and their integrated versions in the context of testing the goodness-of-fit of a heavy tailed distribution function. A comparison of these tests is conducted via Bahadur efficiency and simulations. In the simulations, the score test and the integrated score test show the best performance. Although the Berk-Jones test is more powerful than the Kolmogorov-Smirnov test, this does not hold true for their integrated versions; this differs from results in Einmahl et al. [2003. Empirical likelihood based hypothesis testing. Bernoulli 9(2), 267-290], which shows the difference of Berk-Jones test in testing distributions and tails. http://repub.eur.nl/res/pub/7031/ 2005-11-07T00:00:00Z For testing whether a distribution function is heavy tailed, we study the Kolmogorov test, Berk-Jones test, score test and their integrated versions. A comparison is conducted via Bahadur efficiency and simulations. The score test and the integrated score test show the best performance. Although the Berk-Jones test is more powerful than the Kolmogorov-Smirnov test, this does not hold true for their integrated versions; this differs from results in \\citet{EinmahlMckeague2003}, which shows the difference of Berk-Jones test in testing distributions and tails. http://repub.eur.nl/res/pub/12389/ 2001-02-01T00:00:00Z 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 asymptotic mean-squared error. Unlike previous methods, prior knowledge of the second-order parameter is not required. In addition, we are able to dispense with the need for a prior estimate of the tail index which already converges roughly at the optimal rate. The only arbitrary choice of parameters is the number of Monte Carlo replications. http://repub.eur.nl/res/pub/1650/ 2000-05-25T00:00:00Z Estimators of the extreme-value index are based on a set of upper order statistics. We present an adaptive method to choose the number of order statistics involved in an optimal way, balancing variance and bias components. Recently this has been achieved for the similar but somewhat less involved case of regularly varying tails (Drees and Kaufmann(1997); Danielsson et al.(1996)). The present paper follows the line of proof of the last mentioned paper. http://repub.eur.nl/res/pub/1652/ 2000-05-25T00:00:00Z 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 asymptotic mean squared error. Unlike previous methods, prior knowledge of the second order parameter is not required. In addition, we are able to dispense with the need for a prior estimate of the tail index which already converges roughly at the optimal rate. The only arbitrary choice of parameters is the number of Monte Carlo replications. http://repub.eur.nl/res/pub/12390/ 2000-01-01T00:00:00Z http://repub.eur.nl/res/pub/7711/ 1999-10-14T00:00:00Z The paper characterizes first and second order tail behavior of convolutions of i.i.d. heavy tailed random variables with support on the real line. The result is applied to the problem of risk diversification in portfolio analysis and to the estimation of the parameter in a MA(1) model. http://repub.eur.nl/res/pub/1564/ 1999-03-30T00:00:00Z For samples of random variables with a regularly varying tail estimating the tail index has received much attention recently. For the proof of asymptotic normality of the tail index estimator second order regular variation is needed. In this paper we first supplement earlier results on convolution given by Geluk et al. (1997). Secondly we propose a simple estimator of the tail index for finite moving average time series. We also give a subsampling procedure in order to estimate the optimal sample fraction in the sense of minimal mean squared error. http://repub.eur.nl/res/pub/1547/ 1998-08-13T00:00:00Z We characterize second order regular variation of the tail sum of F together with a balance condition on the tails interms of the behaviour of the characteristic function near zero. http://repub.eur.nl/res/pub/7793/ 1997-09-04T00:00:00Z In certain cases partial sums of i.i.d. random variables with finite variance are better approximated by a sequence of stable distributions with indices \\alpha_n \\to 2 than by a normal distribution. We discuss when this happens and how much the convergence rate can be improved by using penultimate approximations. Similar results are valid for other stable distributions. http://repub.eur.nl/res/pub/7806/ 1997-01-29T00:00:00Z We use a subsample bootstrap method to get a consistent estimate of the asymptotically optimal choice of the sample fraction, in the sense of minimal mean squared error, which is needed for tail index estimation. Unlike previous methods our procedure is fully self contained. In particular, the method is not conditional on an initial consistent estimate of the tail index; and the ratio of the first and second order tail indices is left unrestricted, but we require the ratio to be strictly positive. Hence the current method yields a complete solution to tail index estimation as it is not predicated on a more or less arbitrary choice of the number of highest order statistics.