ASYMPTOTICALLY OPTIMAL BIAS FOR A GENERAL NONLINEARITY IN PAGES TEST

Page's test for the quick detection of a change in distribution is opt imized by utilizing the log-likelihood ratio (LLR) as a detector nonli nearity. For signal detection applications, locally optimal nonlineari ties are optimal as the signal strength gamma goes to zero, however, f or non-zero values of gamma, the performance of Page's test may be imp roved by applying a subtractive bias. The bias that maximizes an asymp totic (i.e., as the average time between false alarm goes to infinity) performance measure for Page's test for a fixed signal strength is de rived for a general detector nonlinearity. Additionally, the bias is d erived to minimize the signal strength required to achieve a desired a symptotic performance. These two methods for choosing the bias are sho wn to be equivalent. The asymptotically optimal bias for the LLR nonli nearity is shown to be zero, which is consistent with the optimality o f the LLR. Subject to a first order approximation, it is shown that th e proposed asymptotically optimal bias is equivalent to an extension o f the bias derived by Dyson [1] which approximately maximizes the rela tive efficiency between Page's test with the biased locally optimal no nlinearity and Page's test with the LLR nonlinearity. The use of the a symptotically optimal bias is illustrated through an example.