Two rank order tests for M-ary detection

We consider a general M-ary detection problem where, given M groups of L samples each, the problem is to identify which unique group of L samples have come from the signal hypothesis. The optimal likelihood ratio test is unrealizable, when the joint distribution of M L samples is not completely known. We consider two rank order types of tests termed the modified rank test (MRT) and the modified rank test with row sort (MRTRS). We examine through simulation, the small sample probability of error performances of MRT and MRTRS for detecting a signal among contaminants. Numerically comparable closed-form error expressions are derived for some special cases. The asymptotic (large sample) error rate of the MRT is also derived. The results indicate that MRTRS provides improved performance over other previously known rank tests.