Non-parametric adaptive locally asymptotically optimum detection in additive noise
In this paper, a new approach to non-parametric signal detection with independent noise sampling is presented. The present approach is based on the locally asymptotically optimum (LAO) methodology, which is valid for vanishingly small signals and very large sample sizes, and on semi-parametric statistics. Its unique feature and essential difference from other techniques is that LAO non-parametric detectors are optimum  according to the NeymanPearson criterion by being asymptotically uniformly most powerful at false alarm level ? ? (AUMP (? ? )) and adaptive in the sense that no loss in Fisher's information number is incurred when the underlying noise process is no longer parametrically defined. Accordingly, they are robust against deviations from the postulated noise model and, unlike other non-parametric detectors, are distribution-free  under both hypotheses H0 H 0 (noise only present) and H1 H 1 (signal and noise present). Non-parametric LAO detectors are derived from an asymptotic stochastic expansion of the log-likelihood ratio for coherent and narrowband incoherent onoff signals. Moreover, under the present framework it is shown that, in direct contrast to already known results, the non-parametric sign detector is AUMP (? ? ) and adaptive even for non-constant signal samples.
adaptive asymptotically uniformly most powerful non-parametric detection coherent and incoherent signals