L. Peng (Liang)
http://repub.eur.nl/ppl/1897/
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http://repub.eur.nl/
RePub, Erasmus University RepositoryGoodness-of-fit tests for a heavy tailed distribution
http://repub.eur.nl/pub/15234/
Mon, 01 Dec 2008 00:00:01 GMT<div>A.J. Koning</div><div>L. Peng</div>
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.Parametric tail copula estimation and model testing
http://repub.eur.nl/pub/64185/
Tue, 01 Jul 2008 00:00:01 GMT<div>L.F.M. de Haan</div><div>C. Neves</div><div>L. Peng</div>
Parametric models for tail copulas are being used for modeling tail dependence and maximum likelihood estimation is employed to estimate unknown parameters. However, two important questions seem unanswered in the literature: (1) What is the asymptotic distribution of the MLE and (2) how does one test the parametric model? In this paper, we answer these two questions in the case of a single parameter for ease of illustration. A simulation study is provided to investigate the finite sample performance of the proposed estimator and test.Goodness-of-fit tests for a heavy tailed distribution
http://repub.eur.nl/pub/7031/
Mon, 07 Nov 2005 00:00:01 GMT<div>A.J. Koning</div><div>L. Peng</div>
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.On optimising the estimation of high quantiles of a probability distribution
http://repub.eur.nl/pub/70210/
Mon, 01 Sep 2003 00:00:01 GMT<div>A. Ferreira</div><div>L.F.M. de Haan</div><div>L. Peng</div>
Using a bootstrap method to choose the sample fraction in tail index estimation
http://repub.eur.nl/pub/12389/
Thu, 01 Feb 2001 00:00:01 GMT<div>J. Danielsson</div><div>L. Peng</div><div>C.G. de Vries</div><div>L.F.M. de Haan</div>
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.Convolutions of heavy-tailed random variables and applications to portfolio diversification and MA(1) time series
http://repub.eur.nl/pub/54286/
Fri, 01 Dec 2000 00:00:01 GMT<div>J.L. Geluk</div><div>L. Peng</div><div>C.G. de Vries</div>
A bootstrap-based method to achieve optimality on estimating the extreme-value index
http://repub.eur.nl/pub/1650/
Thu, 25 May 2000 00:00:01 GMT<div>G. Draisma</div><div>L.F.M. de Haan</div><div>L. Peng</div><div>T.T. Pereira</div>
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.Using a bootstrap method to choose the sample fraction in tail index estimation
http://repub.eur.nl/pub/1652/
Thu, 25 May 2000 00:00:01 GMT<div>J. Danielsson</div><div>L.F.M. de Haan</div><div>L. Peng</div><div>C.G. de Vries</div>
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.Convolutions of heavy-tailed random variables and applications to portfolio diversification and MA(1) time series
http://repub.eur.nl/pub/12390/
Sat, 01 Jan 2000 00:00:01 GMT<div>J.L. Geluk</div><div>L. Peng</div><div>C.G. de Vries</div>
Convolutions of Heavy Tailed Random Variables and Applications to Portfolio Diversification and MA(1) Time Series
http://repub.eur.nl/pub/7711/
Thu, 14 Oct 1999 00:00:01 GMT<div>J.L. Geluk</div><div>L. Peng</div><div>C.G. de Vries</div>
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.An adaptive optimal estimate of the tail index for MA(1) time series
http://repub.eur.nl/pub/1564/
Tue, 30 Mar 1999 00:00:01 GMT<div>J.L. Geluk</div><div>L. Peng</div>
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.Second order regular variation and the domain of attraction of stable distributions
http://repub.eur.nl/pub/1547/
Thu, 13 Aug 1998 00:00:01 GMT<div>J.L. Geluk</div><div>L. Peng</div>
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.Approximation by Penultimate Stable Laws
http://repub.eur.nl/pub/7793/
Thu, 04 Sep 1997 00:00:01 GMT<div>L.F.M. de Haan</div><div>L. Peng</div><div>H. Iglesias Pereira</div>
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.Rates of convergence for bivariate extremes
http://repub.eur.nl/pub/69652/
Thu, 01 May 1997 00:00:01 GMT<div>L.F.M. de Haan</div><div>L. Peng</div>
Under a second order regular variation condition, rates of convergence of the distribution of bivariate extreme order statistics to its limit distribution are given both in the total variation metric and in the uniform metric.Using a Bootstrap Method to choose the Sample Fraction in Tail Index Estimation
http://repub.eur.nl/pub/7806/
Wed, 29 Jan 1997 00:00:01 GMT<div>J. Danielsson</div><div>L.F.M. de Haan</div><div>L. Peng</div><div>C.G. de Vries</div>
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.