Incomplete Samples and Tail Estimation for Stationary Sequences

Abstract. Let (Xn) be a strictly stationary sequence with a marginal distribution function F such that 1 − F (x) = x−αL(x), x > 0, where α > 0 and L(x) is a slowly varying function. We assume that only observations of (Xn) are available at certain points. Under assumption of weak dependency we proved the consistency of Hill’s estimator of the tail index α based on an incomplete sample from {X1, X2 . . . , Xn}. This is an extension of the results of Hsing [15] and Mladenović and Piterbarg [19].