Permutation tests for nonparametric detection

In this paper, the authors provide a methodology to design nonparametric permutation tests and, in particular, nonparametric rank tests for applications in detection. In the first part of the paper, the authors develop the optimization theory of both permutation and rank tests in the Neyman–Pearson sense; in the second part of the paper, they carry out a comparative performance analysis of the permutation and rank tests (detectors) against the parametric ones in radar applications.First, a brief review of some contributions on nonparametric tests is realized. Then, the optimum permutation and rank tests are derived. Finally, a performance analysis is realized by Monte-Carlo simulations for the corresponding detectors, and the results are shown in curves of detection probability versus signal-to-noise ratio.

► Methodology to design nonparametric permutation tests. ► Optimization theory for permutation and rank tests. ► Performance analysis of permutation, rank and parametric detectors. ► The optimum permutation detector is robust and powerful. ► Main problem of permutation detectors: computational complexity.