Optimum detection of a weak signal with minimal knowledge of dependency

The optimum nonlinearity is defined for detection of a weak signal when minimal knowledge of the dependency structure of the observations is available. Specifically, it is assumed that the observations form a one-dependent strictly stationary sequence of random variables and that only a finite number of moments of the marginal density and the correlation coefficient between consecutive observations are known. It is assumed that the bivariate densities involved can be represented as diagonal series, using orthonormal polynomials. Using efficacy as a performance measure, the optimum nonlinearity is required to satisfy a saddle-point condition over this class of bivariate densities.