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

摘要

The limit distribution of the random vector ((M) over tilde (n), M-n), 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 u(n) < v(n), events (<(M)over bar>(n) <= u(n)) and {M-n <= v(n)} are asymptotically independent as n -> infinity, while for other values u(n) < v(n) these events can be asymptotically perfectly dependent.