Extremes of Locally-stationary Chi-square processes on discrete grids

Abstract

For X i (t), i = 1, . . . , n, t ∈ [0, T ] centered Gaussian processes, the chi-square process n i=1 X 2 i (t) appears naturally as limiting processes in various statistical models. In this paper, we are concerned with the exact tail asymptotics of the supremum taken over discrete grids of a class of locally stationary chi-square processes where X i (t), 1 ≤ i ≤ n are not identical. An important tool for establishing our results is a generalisation of Pickands lemma under the discrete scenario.An application related to the change-point problem is discussed.