A two-stage version of the Kassam–Thomas nonparametric dead-zone limiter detection system

A useful modification of the Kassam–Thomas nonparametric dead-zone limiter detection system is proposed. The modified detector is based on a recently established procedure for multistage hypothesis testing which offers improved efficiency over fixed-sample-size tests while retaining the implementational and mismatch advantages that fixed-sample-size tests have over strictly sequential tests. The proposed detector operates as follows: A group of observations is taken and the Kassam–Thomas procedure is applied to decide whether or not a signal is present. If it is decided that no signal is present the procedure stops; otherwise a second group of observations is taken and the test is reperformed in order to double-check the results of the first test. Thus the presence of a signal is announced only when this decision has been double-checked. Two versions of this detector are proposed, one of which discards the first group of observations when double-checking and the other of which performs the double-check on the combined first and second groups. Both detectors are strictly nonparametric. Improvement in performance, in terms of the average number of samples, over the Kassam–Thomas detector is observed. With proper choices of data group sizes and of the significance level for testing the first group of observations, significant improvement can be obtained. These modified detectors are particularly attractive when the prior probability of the signal being absent is very much larger than the prior probability of the signal being present. Under this condition, the asymptotic performance of the proposed detector is better even than that of the linear detector under Gaussian noise in most cases considered. However, these new procedures are strictly nonparametric whereas the linear detector is parametric.