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Non Parametric Confidence Intervals for Receiver Operating Characteristic Curves

Author

Listed:
  • Peter G. Hall
  • Rob J. Hyndman

    ()

  • Yanan Fan

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.

Suggested Citation

  • Peter G. Hall & Rob J. Hyndman & Yanan Fan, 2003. "Non Parametric Confidence Intervals for Receiver Operating Characteristic Curves," Monash Econometrics and Business Statistics Working Papers 12/03, Monash University, Department of Econometrics and Business Statistics.
  • Handle: RePEc:msh:ebswps:2003-12
    as

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    File URL: http://www.buseco.monash.edu.au/ebs/pubs/wpapers/2003/wp12-03.pdf
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    Cited by:

    1. 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.
    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. Òscar Jordà & Alan M. Taylor, 2011. "Performance Evaluation of Zero Net-Investment Strategies," NBER Working Papers 17150, National Bureau of Economic Research, Inc.

    More about this item

    Keywords

    Bandwidth selection; binary classification; kernel estimator; receiver operating characteristic curve.;

    JEL classification:

    • C12 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Hypothesis Testing: General
    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General
    • C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General

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