Opportunistic Detection Under a Fixed-Sample-Size Setting

Abstract

With a finite number of samples drawn from one of two possible distributions sequentially revealed, an opportunistic detection rule is proposed, which possibly makes an early decision in favor of the alternative hypothesis, while always deferring the decision of the null hypothesis until collecting all the samples. Properties of this opportunistic detection rule are discussed and its key asymptotic behavior in the large sample size limit is established. Specifically, a Chernoff-Stein lemma type of characterization of the exponential decay rate of the miss probability under the Neyman-Pearson criterion is established, and consequently, a performance metric of asymptotic exponential efficiency loss is proposed and discussed, which is exactly the ratio between the Kullback-Leibler distance and the Chernoff information of the two hypotheses. Analytical results are corroborated by numerical experiments.