On tail index estimation using a sample with missing observations

For the sequence of heavy-tailed, dependent and heterogeneous random variables with the missing observations the estimation of the tail-index is considered. Under minimal but verifiable assumption of “extremal dependence” we proved the consistency of a geometric-type estimator (Brito and Freitas, 2003). We extended results from Mladenović and Piterbarg (2008) and proved the consistency and the asymptotic normality of the Hill estimator. Illustrative examples are provided.