Robustness of tail index estimation

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, when 2 less than or equal to r + 1 less than or equal to n. This article is concerned with a robust procedure of choosing an optimal r. Thus, an estimation procedure, delta(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.