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Rank statistics expressible as integrals under P–P‐plots and receiver operating characteristic curves

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  • A. J. Girling

Abstract

Given a probability measure on the unit square, the measure of the region under an empirical P–P‐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.

Suggested Citation

  • A. J. Girling, 2000. "Rank statistics expressible as integrals under P–P‐plots and receiver operating characteristic curves," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 62(2), pages 367-382.
    • Handle: RePEc:bla:jorssb:v:62:y:2000:i:2:p:367-382
    DOI: 10.1111/1467-9868.00237
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    Cited by:

    1. Mushkudiani, N.A. & Einmahl, J.H.J., 2004. "Generalized Probability-Probability Plots," Other publications TiSEM 1f85f7ad-3af4-4af2-aa8b-2, Tilburg University, School of Economics and Management.
    2. Mushkudiani, N.A. & Einmahl, J.H.J., 2004. "Generalized Probability-Probability Plots," Discussion Paper 2004-84, Tilburg University, Center for Economic Research.
    3. Jeroen Hinloopen & Rien J.L.M. Wagenvoort & Charles van Marrewijk, 2012. "A k-sample homogeneity test: the Harmonic Weighted Mass index," International Econometric Review (IER), Econometric Research Association, vol. 4(1), pages 17-39, April.

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