Some Optimal CUSUM Rule Extensions in Dynamic Model Parameter Change-point Detection Problems

This paper proposes three extensions of the usual CUSUM rule for change point detection in dynamic systems, in situations where the application of the rule is problematic. The first two ones concern the case of nonlinear state-space systems indirectly observed and the case of uncertain systems. The third one improves the performance of the usual rule when applied to nonstationary systems, by ensuring a constant rate of false alarms. They all rely on kernel-based nonparametric estimation approaches.