Construction of confidence sets with application to classification and some other problems

Abstract

The construction of a confidence set can be applied in many problems. In this study, we are focusing on comparison and classification problems. For comparison problem, we can construct a confidence set for equivalence test and upper confidence bounds on several samples by three methods: using the theorem from Liu et al. (2009), F statistic and Studentized range statistic. For classification problem, we would like to classify a new case into its true class, based on some measurements. Five classification methods have been studied. They are logistic regression, classification tree, Bayesian method, support vector machine and the new confidence set method. The new method constructs a confidence set for the true class for a new case by inverting the acceptance sets. The advantage of this method is that the probability of correct classification is not less than 1􀀀. The methods are illustrated specifically with the well-known Iris data, seeds data and applied to a data set for classifying patients as normal, having fibrosis or having cirrhosis based on some measurements on blood samples. The total misclassification error and sensitivity (true positive rate) are used for comparing the methods.

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Identifiers

ORCID for Wei Liu: orcid.org/0000-0002-4719-0345

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