On estimation of the exponent of regular variation using a sample with missing observations

Abstract

Let (X n) be a sequence of possibly dependent random variables with the same marginal distribution function F, such that 1 - F (x) = x - α L (x), α > 0, where L (x) is a slowly varying function. In this paper the Hill estimator of the exponent of regular variation based on a sample with missing observations from the sequence (X n) is considered. The asymptotic consistency was proved under some general conditions. This extends results of Hsing [1991. On tail index estimation using dependent data. Ann. Statist. 19, 1547-1569]. © 2007 Elsevier B.V. All rights reserved.