Asymptotically robust detection and estimation for very heavy-tailed noise

The asymptotically robust detection of signals and the analogous problem of estimation of location are considered for noise distributions with heavier than exponential tails. The solution to both problems is identical and is obtained when using efficacy or asymptotic variance as the performance measure. The density of the noise is assumed to belong to a E-contamination class where the contaminant is either (1) from the class of unimodal densities, (2) from the class of densities limited in support to an interval about the mode of the nominal density, or (3) a mixture of a member of (1) with a member of (2). The robust detector or estimator is similar to a censored version of the nonlinearity used for maximum-likelihood estimation or locally optimal detection in the presence of noise with the nominal distribution.