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Confidence Sets for Statistical Classification

Author

Listed:
  • Wei Liu

    (S3RI and School of Mathematics, University of Southampton, Highfield, Southampton SO17 1BJ, UK)

  • Frank Bretz

    (Novartis Pharma AG, 4002 Basel, Switzerland
    Visiting address: Center for Medical Statistics, Informatics and Intelligent Systems, Medical University of Vienna, Vienna 1090, Austria.)

  • Natchalee Srimaneekarn

    (S3RI and School of Mathematics, University of Southampton, Highfield, Southampton SO17 1BJ, UK)

  • Jianan Peng

    (Department of Mathematics and Statistics, Acadia University, Wolfville, NS B4P 2R6, Canada)

  • Anthony J. Hayter

    (Department of Statistics and Operations Technology, University of Denver, Denver, CO 80208-8921, USA)

Abstract

Classification has applications in a wide range of fields including medicine, engineering, computer science and social sciences among others. In statistical terms, classification is inference about the unknown parameters, i.e., the true classes of future objects. Hence, various standard statistical approaches can be used, such as point estimators, confidence sets and decision theoretic approaches. For example, a classifier that classifies a future object as belonging to only one of several known classes is a point estimator. The purpose of this paper is to propose a confidence-set-based classifier that classifies a future object into a single class only when there is enough evidence to warrant this, and into several classes otherwise. By allowing classification of an object into possibly more than one class, this classifier guarantees a pre-specified proportion of correct classification among all future objects. An example is provided to illustrate the method, and a simulation study is included to highlight the desirable feature of the method.

Suggested Citation

  • Wei Liu & Frank Bretz & Natchalee Srimaneekarn & Jianan Peng & Anthony J. Hayter, 2019. "Confidence Sets for Statistical Classification," Stats, MDPI, vol. 2(3), pages 1-15, June.
    • Handle: RePEc:gam:jstats:v:2:y:2019:i:3:p:24-346:d:244564
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    References listed on IDEAS

    as
    1. Fang Wan & Wei Liu & Frank Bretz & Yang Han, 2016. "Confidence sets for optimal factor levels of a response surface," Biometrics, The International Biometric Society, vol. 72(4), pages 1285-1293, December.
    2. Mauricio Sadinle & Jing Lei & Larry Wasserman, 2019. "Least Ambiguous Set-Valued Classifiers With Bounded Error Levels," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 114(525), pages 223-234, January.
    3. W. Liu & Y. Han & F. Bretz & F. Wan & P. Yang, 2016. "Counting by weighing: know your numbers with confidence," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 65(4), pages 641-648, August.
    4. Jing Lei, 2014. "Classification with confidence," Biometrika, Biometrika Trust, vol. 101(4), pages 755-769.
    Full references (including those not matched with items on IDEAS)

    Citations

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    Cited by:

    1. Wei Liu & Frank Bretz & Anthony J. Hayter, 2019. "Confidence Sets for Statistical Classification (II): Exact Confidence Sets," Stats, MDPI, vol. 2(4), pages 1-8, November.

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