Back to the local score in the logarithmic case : a direct and simple proof

Jean-Noel BACRO, Jean-Jacques DAUDIN, Sabine MERCIER, Stéphane ROBIN

Ann. Inst. Statist. Math, 2002.


Let X1, ... Xn be a sequence of i.i.d. positive or negative integer valued random variables and Hn = max0 <= i <= j <= n(Xi + ... + Xj) the local score of the sequence. A recent result shows that Hn is actually the maximum of an integer valued Lindley process. Therefore known results about the asymptotic distribution of the maximum of a weakly dependent process give readily the expected result about the asymptotic behavior of the local score, with a simple way for computing the needed constants.

Key words and phrases Extremal index, Lindley process, local score, Markov chain