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Estimation of a convex ROC curve

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  • Lloyd, Chris J.

Abstract

The receiver operating characteristic curve summarises the accuracy of a binary classifier. Provided that the group probabilities are monotonically related to the diagnostic, it is well known that the receiver operating characteristic (ROC) curve is convex. This article presents a method of computing the maximum likelihood estimator of the ROC curve assuming convexity. Firstly, the estimator is of interest in its own right, when it is believed that the decision variable is monotonically related to the likelihood of disease. Bias and standard error may be estimated using a simply implemented bootstrap technique. Secondly, the new estimator also leads naturally and directly to a new family of non-parametric tests of convexity.

Suggested Citation

  • Lloyd, Chris J., 2002. "Estimation of a convex ROC curve," Statistics & Probability Letters, Elsevier, vol. 59(1), pages 99-111, August.
    • Handle: RePEc:eee:stapro:v:59:y:2002:i:1:p:99-111
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    References listed on IDEAS

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    1. Lloyd, Chris J. & Yong, Zhou, 1999. "Kernel estimators of the ROC curve are better than empirical," Statistics & Probability Letters, Elsevier, vol. 44(3), pages 221-228, September.
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    Cited by:

    1. Rufibach Kaspar, 2012. "A Smooth ROC Curve Estimator Based on Log-Concave Density Estimates," The International Journal of Biostatistics, De Gruyter, vol. 8(1), pages 1-29, April.
    2. Alicja Jokiel-Rokita & Rafał Topolnicki, 2019. "Minimum distance estimation of the binormal ROC curve," Statistical Papers, Springer, vol. 60(6), pages 2161-2183, December.
    3. Zhang, Biao, 2006. "A semiparametric hypothesis testing procedure for the ROC curve area under a density ratio model," Computational Statistics & Data Analysis, Elsevier, vol. 50(7), pages 1855-1876, April.

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