In this paper, we investigate the limiting distribution of the locations related with high values generated by a strictly stationary sequence of random variables. The main tool for this purpose is the so-called local extremes comparison lemma, which enables us to obtain the convergence in distribution of various functionals related with the location of extreme order statistics, including the location of local maxima and the joint locations of the largest order statistics. Furthermore, results about the joint asymptotic behavior of the location of the first high-level exceedance and the location of the maximum are also discussed.

CEMAT - Center for Computational and Stochastic Mathematics