Opportunistic detection rules

Opportunistic detection rules (ODRs) are variants of fixed-sample-size detection rules in which the statistician is allowed to make an early decision on the alternative hypothesis opportunistically based on the sequentially observed samples. From a sequential decision perspective, ODRs are also mixtures of one-sided and truncated sequential detection rules. Several key properties of ODRs are established in this paper, in both the asymptotic regime in which the maximum sample size grows without bound, and the finite regime in which the maximum samples size is a fixed finite number. Furthermore, an extended setup, in which the maximum sample size is a random variable following a geometric distribution whose realization is not revealed to the statistician until observing the last sample, is studied.