Using a bootstrap method to choose the sample fraction in tail index estimation
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.
|Keywords||bias, bootstrap, mean squared error, optimal extreme sample fraction, tail index|
|Persistent URL||dx.doi.org/10.1006/jmva.2000.1903, hdl.handle.net/1765/12389|
Danielsson, J., Peng, L., de Vries, C.G., & de Haan, L.F.M.. (2001). Using a bootstrap method to choose the sample fraction in tail index estimation. Journal of Multivariate Analysis, 76(2), 226–248. doi:10.1006/jmva.2000.1903