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Nonparametric confidence intervals for receiver operating characteristic curves

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  • Peter Hall

Abstract

We study methods for constructing confidence intervals and confidence bands for estimators of receiver operating characteristics. Particular emphasis is placed on the way in which smoothing should be implemented, when estimating either the characteristic itself or its variance. We show that substantial undersmoothing is necessary if coverage properties are not to be impaired. A theoretical analysis of the problem suggests an empirical, plug-in rule for bandwidth choice, optimising the coverage accuracy of interval estimators. The performance of this approach is explored. Our preferred technique is based on asymptotic approximation, rather than a more sophisticated approach using the bootstrap, since the latter requires a multiplicity of smoothing parameters all of which must be chosen in nonstandard ways. It is shown that the asymptotic method can give very good performance. Copyright Biometrika Trust 2004, Oxford University Press.

Suggested Citation

  • Peter Hall, 2004. "Nonparametric confidence intervals for receiver operating characteristic curves," Biometrika, Biometrika Trust, vol. 91(3), pages 743-750, September.
  • Handle: RePEc:oup:biomet:v:91:y:2004:i:3:p:743-750
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    Cited by:

    1. Yunguo Lu & Lin Zhang, 2023. "Environmental information disclosure and firm production: evidence from the estimated efficiency of publicly listed firms in China," Journal of Productivity Analysis, Springer, vol. 59(1), pages 99-119, February.
    2. Gong, Yun & Peng, Liang & Qi, Yongcheng, 2010. "Smoothed jackknife empirical likelihood method for ROC curve," Journal of Multivariate Analysis, Elsevier, vol. 101(6), pages 1520-1531, July.
    3. Lahiri, Kajal & Wang, J. George, 2013. "Evaluating probability forecasts for GDP declines using alternative methodologies," International Journal of Forecasting, Elsevier, vol. 29(1), pages 175-190.
    4. Kajal Lahiri & Liu Yang, 2018. "Confidence Bands for ROC Curves With Serially Dependent Data," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 36(1), pages 115-130, January.
    5. Òscar Jordà & Alan M. Taylor, 2011. "Performance Evaluation of Zero Net-Investment Strategies," NBER Working Papers 17150, National Bureau of Economic Research, Inc.
    6. Eugene Demidenko, 2012. "Confidence intervals and bands for the binormal ROC curve revisited," Journal of Applied Statistics, Taylor & Francis Journals, vol. 39(1), pages 67-79, March.
    7. Kaushik Ghosh & Ram Tiwari, 2007. "Empirical process approach to some two-sample problems based on ranked set samples," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 59(4), pages 757-787, December.
    8. Dag Kolsrud, 2007. "Time-simultaneous prediction band for a time series," Journal of Forecasting, John Wiley & Sons, Ltd., vol. 26(3), pages 171-188.
    9. Lopez-de-Ullibarri, Ignacio & Cao, Ricardo & Cadarso-Suarez, Carmen & Lado, Maria J., 2008. "Nonparametric estimation of conditional ROC curves: Application to discrimination tasks in computerized detection of early breast cancer," Computational Statistics & Data Analysis, Elsevier, vol. 52(5), pages 2623-2631, January.
    10. J. M. Azaïs & S. Bercu & J. C. Fort & A. Lagnoux & P. Lé, 2010. "Simultaneous confidence bands in curve prediction applied to load curves," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 59(5), pages 889-904, November.

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