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Rank statistics expressible as integrals under PP-plots and receiver operating characteristic curves

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Given a probability measure on the unit square, the measure of the region under an empirical PP-plot defines a two-sample rank statistic. Instances include trimmed and censored versions of the Mann–Whitney–Wilcoxon statistic and a class of statistics with applications in the analysis of receiver operating characteristic (ROC) curves. A large sample distribution for such a statistic is obtained, which is valid under sampling from general populations. Explicit results are presented for comparing arbitrary quantile segments of two populations. The results are not restricted to continuous data and incorporate adjustments for tied values in the discrete case. A multivariate version of the large sample distribution extends the class of tractable statistics in ROC analysis and facilitates the use of methods based on partial areas when the data are discrete.
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Keywords: Partial areas; P–P-plot; Rank statistics; Receiver operating characteristic; Trimming; Type II censoring

Document Type: Research Article

Affiliations: University of Birmingham, UK

Publication date: February 1, 2000

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