An efficient nonparametric detector based on a three-sample classification model

The proposed detector uses three vector samples to decide which one of two distinct stationary or quasi-stationary stochastic processes is present at its input. A reference sample is obtained from each of the two processes during an initial learning interval, and the third sample is taken on the decision interval. It is assumed that independent samples can be obtained from the stochastic processes. A weighted linear combination of two
2
-sample Mann-Whitney statistics defined on the three vector samples is used at the detector. An upper bound on the asymptotic or large-sample error probability is obtained, which indicates that, unlike the
2
-sample detector, the new detector is insensitive to the {\em a priori} signal probability and operates well in an unspecified environment. Comparisons are made between the proposed model and the standard
2
-sample model at both small and large values of signal-to-noise ratio. An extension to intermediate values of signal-to-noise ratio is obtained by considering two examples, dc signal in additive noise and Lehmann's nonparametric class of alternatives. Owing mainly to an invariant optimum threshold setting, the proposed procedure results in a significantly better performance over a wide range of signal-to-noise ratio.