ABSTRACT
This chapter is concerned with the problem of minimizing the moments of the detection delay, in pointwise (i.e., for all change points) and minimax (i.e., for a worst change point) settings among all procedures for which the local probability of a false alarm in the fixed time window is upper-bounded by a given small number. It shows that the mixture version of the Shiryaev–Roberts rule (MSR) is asymptotically optimal in the class of procedures with the prescribed maximal conditional probability of false alarm when it is small, minimizing moments of the detection delay pointwise (for all change points) as well as in a minimax sense. An important feature of the MSR rule is applicability of a simple upper bound on the probability of false alarm.
