Confidence Sets for Statistical Classification (II): Exact Confidence Sets

Wei Liu, Frank Bretz and Anthony J. Hayter
Additional contact information
Wei Liu: S3RI, School of Mathematics University of Southampton, Southampton SO17 1BJ, UK
Frank Bretz: Novartis Pharma AG, 4002 Basel, Switzerland
Anthony J. Hayter: Department of Statistics and Operations Technology, University of Denver, Denver, CO 80208, USA

Stats, 2019, vol. 2, issue 4, 1-8

Abstract: Classification has applications in a wide range of fields including medicine, engineering, computer science and social sciences among others. Liu et al. (2019) proposed 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. However, the classifier uses a conservative critical constant. In this paper, we show how to determine the exact critical constant in applications where prior knowledge about the proportions of the future objects from each class is available. As the exact critical constant is smaller than the conservative critical constant given by Liu et al. (2019), the classifier using the exact critical constant is better than the classifier by Liu et al. (2019) as expected. An example is provided to illustrate the method.

Keywords: classification; confidence level; confidence set; coverage frequency; statistical inference (search for similar items in EconPapers)
JEL-codes: C1 C10 C11 C14 C15 C16 (search for similar items in EconPapers)
Date: 2019
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