In this paper we review several results of the nonparametric receiver operating characteristic (ROC) analysis and present an extension to the nonparametric localization ROC (LROC) analysis. Equations for the estimation of the area under the characteristic curve and for the variance calculations are derived. Expressions for the choice of the optimal ratio between the number of signal-absent and signal-present image samples are also presented. The results can be applied both with continuous or discrete scoring scales. The simulation studies carried out validate the theoretical derivations and show that the LROC analysis is considerably more sensitive than the ROC analysis.