New results on large sample performance of counting rules

We consider a decentralized detection problem where a set of n identical sensors send binary information to a fusion center for deciding one of two possible hypotheses, based on Neyman-Pearson criterion. Sensor observations are identical and independent, conditioned on a hypothesis. For a counting rule at the fusion center, we provide new results on the miss error probability, as n increases without bound. The asymptotic error rate of a proportional threshold counting rule is derived. For two detection problems, estimates of asymptotic errors of OR and AND rules are also derived.