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Using a Bootstrap Method to Choose the Sample Fraction in Tail Index Estimation

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  • Danielsson, J.
  • de Haan, L.
  • Peng, L.
  • de Vries, C. G.

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.

Suggested Citation

  • Danielsson, J. & de Haan, L. & Peng, L. & de Vries, C. G., 2001. "Using a Bootstrap Method to Choose the Sample Fraction in Tail Index Estimation," Journal of Multivariate Analysis, Elsevier, vol. 76(2), pages 226-248, February.
    • Handle: RePEc:eee:jmvana:v:76:y:2001:i:2:p:226-248
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