Barndorff-Nielsen's form of the Law of the Iterated Logarithm for r th Moving Maxima

Abstract

Abtsrcat

Let {X_n} be a sequence of independent identically distributed random variables, defined over a common probability space (Ω,ℱ,P) with a continuous distribution function F and let η _r,n denote the r ^th upper order statistic among (X_n-an+1,X_n-an+2,...X_n); n, ≥ 1, where {a _n } is a non-decreasing sequence of integers such that 0 < a _n ≤ n. For a large class of distributions, we obtain Barndor-Nielson's form of the law of the iterated logarithm for {η _r,n }.