Two-stage Wilcoxon detectors using conditional tests

The idea of the Wilcoxon detector using a conditional test is extended to two-stage detectors, which constitute a class of sequential detectors. Three different two-stage detectors are considered, using the Wilcoxon statistic with conditional tests. The three detectors differ in the usage of the samples of the first stage for computing the test statistic in the second stage. In computing the test statistic in the second stage, the first detector disregards all the samples of the first stage, the second detector uses the value of the test statistic of the first stage, and the third detector uses all the samples of the first stage. The asymptotic relative efficiency improves from the first to the second detector. Comparisons of these detectors with fixed-sample-size (FSS) detectors show that they are better than both the FSS linear detector and the FSS conditional Wilcoxon detector under the same false-alarm and detection probabilities