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Using a bootstrap method to choose the sample fraction in tail index estimation

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Author Info
J. Danielsson
L. de Haan ()
L. Peng
C.G. de Vries (FEW-Econometrie en besliskunde)

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Abstract

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.

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Paper provided by Erasmus University Rotterdam, Econometric Institute in its series Econometric Institute Report with number 197.

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Date of creation: 2000
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Handle: RePEc:dgr:eureir:2000197

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Keywords: tail index bootstrap bias mean squared error;

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  1. Dekkers, A. L. M. & Dehaan, L., 1993. "Optimal Choice of Sample Fraction in Extreme-Value Estimation," Journal of Multivariate Analysis, Elsevier, vol. 47(2), pages 173-195, November. [Downloadable!] (restricted)
  2. Vries, Caspar de & Danielsson, Jon, 1996. "Tail Index and Quantile Estimation with Very High Frequency Data," CESifo Working Paper Series CESifo Working Paper No. , CESifo Group Munich.
  3. Hall, Peter, 1990. "Using the bootstrap to estimate mean squared error and select smoothing parameter in nonparametric problems," Journal of Multivariate Analysis, Elsevier, vol. 32(2), pages 177-203, February. [Downloadable!] (restricted)
  4. Jansen, Dennis W & de Vries, Casper G, 1991. "On the Frequency of Large Stock Returns: Putting Booms and Busts into Perspective," The Review of Economics and Statistics, MIT Press, vol. 73(1), pages 18-24, February. [Downloadable!] (restricted)
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