On the score functions of the two-sample locally optimum rank test statistic for random signals in additive noise

The test statistic of the two-sample locally optimum rank detector is derived for weak random signals in additive noise. It is shown that the two-sample locally optimum rank detector for random signals has interesting similarities to the one-sample locally optimum rank detector for random signals. The detector may also be viewed as a generalization of the two-sample locally optimum rank detector for known signals. Some examples and properties of the score functions constituting the locally optimum rank test statistic are investigated