Asymptotic efficiency and stability of nonparametric detection rules, based on empirical distribution functions

Bahadur's (1960) stochastic-comparison method is used to examine the Pitman efficiencies of four nonparametric detection rules: the Kolmogorov-Smirnov, omega-squared Mises, Watson, and Wilcoxen rules. Exact expressions of the efficiency measures for these rules are obtained for the following types of noise distributions: normal, exponential, logistic, Cauchy, and chi-squared with r degrees of freedom. The stability of the detection rules with respect to the type of noise is evaluated.