Asymptotic performance measures for sequential partition detectors

It is known that the sequential probability ratio test (SPRT) minimizes the average detection time among all tests for fixed type I and type II errors under the hypothesis and alternative. Often, in practical detection problems, the signal level is unknown during the decision interval. In this paper, the relative efficiency of a sequential detector is compared with its fixed sample size detector counterpart for signal levels which may be inconsistent with the assumed alternative. The results are applicable to detectors called partition detectors which are designed based on knowledge of a set of quantiles and related functions from the unknown noise field, and guarantee distribution-free performance under the hypothesis. For the class of sequential detectors that have boundaries which are linear functions of the sample size, the operating characteristic function and average sample number ASN are derived.