On Estimation and Testing for Pareto Tails

2010 Mathematics Subject Classification: 62F10, 62F12.

The t-Hill estimator for independent data was introduced by Fabian and Stehlik (2009). It estimates the extreme value index of distribution function with regularly varying tail. This paper considers sampling of an infinite moving average model. We prove that in the discussed case the t-Hill estimator is weak consistent. However, in contrast to independent identically distributed case here it is shown that the t-Hill and the Hill estimator applied to the moving average model are not robust with respect to large observations.