We present a general methodology for developing an asymptotically distribution-free, asymptotic minimax tests. The tests are constructed via a nonparametric density-quantile function and the
limiting distribution is derived by a martingale approach. The procedure can be viewed as a novel parametric extension of the classical parametric likelihood ratio test. The proposed tests are shown to be omnibus within an extremely large class of nonparametric global alternatives characterized by simple conditions. Furthermore, we establish that the proposed tests provide better minimax distinguishability. The tests have much greater power for detecting high-frequency nonparametric alternatives than the existing classical tests such as Kolmogorov-Smirnov and Cramer-von Mises tests. The good
performance of the proposed tests is demonstrated by Monte Carlo simulations and applications in High Energy Physics.
