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Kernel estimators of the ROC curve are better than empirical

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  • Lloyd, Chris J.
  • Yong, Zhou
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    Abstract

    The receiver operating characteristic (ROC) is a curve used to summarise the performance of a binary decision rule. It can be expressed in terms of the underlying distributions functions of the diagnostic measurement that underlies the rule. Lloyd (1998) has proposed estimating the ROC curve from kernel smoothing of these distribution functions and has presented asymptotic formulas for the bias and standard deviation of the resulting curve estimator. This paper compares the asymptotic accuracy of the kernel-based estimator with the fully empirical estimator. It is shown that the empirical estimator is deficient compared to the kernel estimator and that this deficiency is unbounded as sample size increases. A simulation study using both unimodal and bimodal distributions indicates that the gains in accuracy are significant for realistic sample sizes. Kernel-based ROC estimators can now be recommended.

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    Bibliographic Info

    Article provided by Elsevier in its journal Statistics & Probability Letters.

    Volume (Year): 44 (1999)
    Issue (Month): 3 (September)
    Pages: 221-228

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    Handle: RePEc:eee:stapro:v:44:y:1999:i:3:p:221-228

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    Related research

    Keywords: Relative deficiency Empirical estimator Kernel estimator ROC curve;

    References

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    1. Donald Dorfman & Edward Alf, 1968. "Maximum likelihood estimation of parameters of signal detection theory—A direct solution," Psychometrika, Springer, vol. 33(1), pages 117-124, March.
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    Cited by:
    1. Lloyd, Chris J., 2002. "Estimation of a convex ROC curve," Statistics & Probability Letters, Elsevier, vol. 59(1), pages 99-111, August.
    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. Yousef, Waleed A. & Kundu, Subrata & Wagner, Robert F., 2009. "Nonparametric estimation of the threshold at an operating point on the ROC curve," Computational Statistics & Data Analysis, Elsevier, vol. 53(12), pages 4370-4383, October.
    4. Peter Hall & Rob J. Hyndman, 2002. "An Improved Method for Bandwidth Selection when Estimating ROC Curves," Monash Econometrics and Business Statistics Working Papers 11/02, Monash University, Department of Econometrics and Business Statistics.
    5. Hall, Peter G. & Hyndman, Rob J., 2003. "Improved methods for bandwidth selection when estimating ROC curves," Statistics & Probability Letters, Elsevier, vol. 64(2), pages 181-189, August.

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