Relative efficiency of the sequential probability ratio test in signal detection

Abstract

The relative efficiency of a sequential hypothesis test compared to a fixed sample size test is defined as the ratio of the expected sample size of the sequential test to the sample size of the fixed sample size test with the same size and power. Asymptotic behavior of the relative efficiency is studied for the detection of a constant signal in additive noise. With some regularity conditions imposed on the noise density, the asymptotic relative efficiency of the sequential probability ratio test with respect to the corresponding fixed sample size likelihood ratio test is a function of the size and the power. As the size a approaches zero and the power approaches unity, this asymptotic relative efficiency has a limiting value depending on the functional relationship of a and 1 - \beta as they approach zero. Comparison of the power functions is also studied.