Detector Relative Efficiencies in the Presence of Laplace Noise

The closed-form solution for Neyman-Pearson optimal detectorperformance for Laplace noise affords a rare opportunity for smalland intermediate sample relative efficiency studies. Indeed, the Laplace noise solution is the only known closed-form description fora non-Gaussian optimal detector of the type considered. Weillustrate numerically that, for stringent detector requirements,convergence of detector relative efficiencies to the correspondingasymptotic values can be quite slow. Three types of asymptoticefficiencies are considered in this comparison of the optimal, linear,and sign detectors.