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

✍ Scribed by J. Danielsson; L. de Haan; L. Peng; C.G. de Vries

Publisher
Elsevier Science
Year
2001
Tongue
English
Weight
163 KB
Volume
76
Category
Article
ISSN
0047-259X

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✦ Synopsis

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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