An empirical likelihood-based CUSUM for on-line model change detection

Abstract

In change detection problem, the distribution of a series of observations can change at some unknown instant. The aim of on-line change detection rule is to detect this change, as rapidly as possible, while ensuring a low rate of false alarm. The most popular rule to treat this problem is the Page’s CUSUM rule. The use of this rule supposes that the two distributions, before and after the change, are known, which is often restrictive in practice. In this article, a nonparametric rule is proposed. Only two learning samples, characterizing the in-control and the out-of-control functioning modes of the system, are needed to implement the rule. The new detection approach is based on the use of a well-known nonparametric method, Empirical Likelihood. Some numerical studies show the relevance of our approach, especially when the size of the learning samples are quite small.