Maximum of a partial sample in the uniform AR(1) processes

Abstract

The limit distribution of the random vector (over(M, ̃)n, Mn), whose components are maximum of the sub-sample with even indices and maximum of the full sample from the uniform AR(1) process with parameter r ≥ 2, is determined. For some values un < vn, events {over(M, ̃)n ≤ un} and {Mn ≤ vn} are asymptotically independent as n → ∞, while for other values un < vn these events can be asymptotically perfectly dependent. © 2009 Elsevier B.V. All rights reserved.