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This paper treats the problem of detecting a signal of known form in the presence of additive noise whose distribution function may not be known. Two detection schemes are considered, one for a signal which is known exactly and one for a signal with unknown phase. Using the criterion of asymptotic relative efficiency (ARE), the performance of each detector is compared with that of the corresponding detector which is optimum for Gaussian noise. It is shown that for detecting a known signal, the ARE of the nonparametric detector relative to the correlation detector is equal to one if the noise is Gaussian, and is strictly greater than one for any continuous non-Gaussian noise distribution. An identical result holds for the ARE of the nonparametric detector for a signal with unknown phase relative to the standard envelope detector.