Example of density estimation kernels and their corresponding rank function [Eq. (10)] for three different values of the smoothing parameter .
Comparison between the model function (top) and their corresponding ROC and LROC curves (bottom) for the two test cases considered.
Distribution of the and estimates obtained by Monte Carlo simulation for the two test cases considered. The theoretical values are marked on the graph.
The distribution of the standard estimates , obtained by Monte Carlo simulation for the two test cases considered (left case 1, right case 2). The theoretical values are marked on the graphs.
Comparison between the ROC and LROC values of as a function of the number of samples and , for the two test cases considered. The plotted curves are isolines on the 3-D surfaces defined by as a function of and for several representative values marked on the plots.
The ratio (left) as a function of the total number of samples for the optimal ratio for the ROC and LROC tests, respectively. On the right are shown the plots of as a function of for the optimal ratios for the comparison between the specific two test cases considered.
Summary of the results obtained for the two test cases considered, with and signal-present and signal-absent, respectively, samples.
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