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

##### Danielsson, J., L. de Haan, L. Peng, and C. de Vries (2001). Using a bootstrap method to choose the sample fraction in tail index estimation. Journal of Multivariate Analysis 76.

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.

```@article{DanielssonHaanPengVries2001,
title={Using a bootstrap method to choose the sample fraction in tail index estimation},
author={J. Danielsson and L. de Haan and L. Peng and C.G. de Vries},
journal={Journal of Multivariate Analysis},
volume=76,
year=2001,
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. },

}
```

The cost of conservatism: Extreme returns, Value-at-Risk, and the {Basle} multiplication factor
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##### Risk research
Jon Danielson's research papers on systemic risk, artificial intelligence, risk forecasting, financial regulations and crypto currencies.