IDEAS home Printed from https://ideas.repec.org/a/plo/pone00/0251959.html
   My bibliography  Save this article

Smooth ROC curve estimation via Bernstein polynomials

Author

Listed:
  • Dongliang Wang
  • Xueya Cai

Abstract

The receiver operating characteristic (ROC) curve is commonly used to evaluate the accuracy of a diagnostic test for classifying observations into two groups. We propose two novel tuning parameters for estimating the ROC curve via Bernstein polynomial smoothing of the empirical ROC curve. The new estimator is very easy to implement with the naturally selected tuning parameter, as illustrated by analyzing both real and simulated data sets. Empirical performance is investigated through extensive simulation studies with a variety of scenarios where the two groups are both from a single family of distributions (symmetric or right skewed) or one from a symmetric and the other from a right skewed distribution. The new estimator is uniformly more efficient than the empirical ROC estimator, and very competitive to eleven other existing smooth ROC estimators in terms of mean integrated square errors.

Suggested Citation

  • Dongliang Wang & Xueya Cai, 2021. "Smooth ROC curve estimation via Bernstein polynomials," PLOS ONE, Public Library of Science, vol. 16(5), pages 1-12, May.
    • Handle: RePEc:plo:pone00:0251959
    DOI: 10.1371/journal.pone.0251959
    as

    Download full text from publisher

    File URL: https://journals.plos.org/plosone/article?id=10.1371/journal.pone.0251959
    Download Restriction: no
    File URL: https://journals.plos.org/plosone/article/file?id=10.1371/journal.pone.0251959&type=printable
    Download Restriction: no
    File URL: https://libkey.io/10.1371/journal.pone.0251959?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    References listed on IDEAS

    as
    1. 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.
    2. Alexandre Leblanc, 2012. "On estimating distribution functions using Bernstein polynomials," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 64(5), pages 919-943, October.
    3. Michał Pulit, 2016. "A new method of kernel-smoothing estimation of the ROC curve," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 79(5), pages 603-634, July.
    4. Zhong Guan, 2016. "Efficient and robust density estimation using Bernstein type polynomials," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 28(2), pages 250-271, June.
    5. Cheng, Cheng, 1995. "The Bernstein polynomial estimator of a smooth quantile function," Statistics & Probability Letters, Elsevier, vol. 24(4), pages 321-330, September.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Dietmar Pfeifer & Olena Ragulina, 2020. "Adaptive Bernstein Copulas and Risk Management," Papers 2011.00909, arXiv.org, revised Mar 2021.
    2. Dietmar Pfeifer & Olena Ragulina, 2020. "Adaptive Bernstein Copulas and Risk Management," Mathematics, MDPI, vol. 8(12), pages 1-22, December.
    3. Ouimet, Frédéric, 2021. "Asymptotic properties of Bernstein estimators on the simplex," Journal of Multivariate Analysis, Elsevier, vol. 185(C).
    4. Frédéric Ouimet, 2021. "General Formulas for the Central and Non-Central Moments of the Multinomial Distribution," Stats, MDPI, vol. 4(1), pages 1-10, January.
    5. Aurélie Bertrand & Ingrid Van Keilegom & Catherine Legrand, 2019. "Flexible parametric approach to classical measurement error variance estimation without auxiliary data," Biometrics, The International Biometric Society, vol. 75(1), pages 297-307, March.
    6. Bertrand, Aurelie & Van Keilegom, Ingrid & Legrand, Catherine, 2017. "Flexible parametric approach to classical measurement error variance estimation without auxiliary data," LIDAM Discussion Papers ISBA 2017025, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    7. Zhong Guan, 2017. "Bernstein polynomial model for grouped continuous data," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 29(4), pages 831-848, October.
    8. Oke Gerke, 2020. "Nonparametric Limits of Agreement in Method Comparison Studies: A Simulation Study on Extreme Quantile Estimation," IJERPH, MDPI, vol. 17(22), pages 1-14, November.
    9. Cheng, Xueqin & Li, Yanpeng, 2022. "An improved Hoeffding’s inequality for sum of independent random variables," Statistics & Probability Letters, Elsevier, vol. 183(C).
    10. Elisa–María Molanes-López & Ricardo Cao, 2008. "Relative density estimation for left truncated and right censored data," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 20(8), pages 693-720.
    11. 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.
    12. Lina Wang & Dawei Lu, 2023. "Application of Bernstein Polynomials on Estimating a Distribution and Density Function in a Triangular Array," Methodology and Computing in Applied Probability, Springer, vol. 25(2), pages 1-14, June.
    13. Cheng, Cheng, 2002. "Almost-sure uniform error bounds of general smooth estimators of quantile density functions," Statistics & Probability Letters, Elsevier, vol. 59(2), pages 183-194, September.
    14. Ariane Hanebeck & Bernhard Klar, 2021. "Smooth distribution function estimation for lifetime distributions using Szasz–Mirakyan operators," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 73(6), pages 1229-1247, December.
    15. 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.
    16. Zielinski, Ryszard, 1999. "Best equivariant nonparametric estimator of a quantile," Statistics & Probability Letters, Elsevier, vol. 45(1), pages 79-84, October.
    17. Paolo Brunori & Guido Neidhöfer, 2021. "The Evolution of Inequality of Opportunity in Germany: A Machine Learning Approach," Review of Income and Wealth, International Association for Research in Income and Wealth, vol. 67(4), pages 900-927, December.
    18. Cheng, Cheng, 1998. "A Berry-Esséen-type theorem of quantile density estimators," Statistics & Probability Letters, Elsevier, vol. 39(3), pages 255-262, August.
    19. Cheam, Amay S.M. & McNicholas, Paul D., 2016. "Modelling receiver operating characteristic curves using Gaussian mixtures," Computational Statistics & Data Analysis, Elsevier, vol. 93(C), pages 192-208.
    20. Funke, Benedikt & Palmes, Christian, 2017. "A note on estimating cumulative distribution functions by the use of convolution power kernels," Statistics & Probability Letters, Elsevier, vol. 121(C), pages 90-98.

    More about this item

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:plo:pone00:0251959. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: plosone (email available below). General contact details of provider: https://journals.plos.org/plosone/ .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.