Properties of the Hill extremal index estimate for samples with pollutions / I. V. Rodionov. //Vestnik Moskovskogo Universiteta. Seriya 1. Matematika. Mekhanika. 2014. № 1. P. 3-6 [Moscow Univ. Math. Bulletin. Vol. 69, N 1, 2014.].
In this paper we consider the consistency and asymptotic normality of the Hill estimator of the extreme value index for a sample from the sequence of independent and identically distributed random variables with asymptotically increasing additive pollution. In addition, the cases when the statistical construction of the estimator is possible are analyzed.
Key words: extreme value index, Hill estimator, consistency, asymptotic normality, additive pollution.