Robustness of Tail Index Estimation - Hsieh,Ping-Hung (Journal of Computational and Graphical Statistics, 1999)
The implementation of the Hill estimator, which estimates the heaviness of the tail of a distribution, requires a choice of the number of extreme observations in the tails, $r$, from a sample of size $n$, where $2 ≤ r+1 ≤ n$. This article is concerned with a robust procedure of choosing an optimal $r$. Thus, an estimation procedure, $δ_s$, based on the idea of spacing statistics, $H^{(r)}$, is developed. The proposed decision rule for choosing $r$ under the squared error loss is found to be a simple function of the sample size. The proposed rule is then illustrated across a wide range of data, including insurance claims, currency exchange rate returns, and city size.
Keywords: Supply Chain