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

Construction of confidence sets with application to classification and some other problems
Construction of confidence sets with application to classification and some other problems
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.
University of Southampton
Srimaneekarn, Natchalee
b9de2ced-ae51-4ac7-a9ab-92c91253640e
Srimaneekarn, Natchalee
b9de2ced-ae51-4ac7-a9ab-92c91253640e
Liu, Wei
b64150aa-d935-4209-804d-24c1b97e024a

Srimaneekarn, Natchalee (2017) Construction of confidence sets with application to classification and some other problems. University of Southampton, Doctoral Thesis, 119pp.

Record type: Thesis (Doctoral)

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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Construction of Confidence sets with Application to Classification and Some Other Problems - Version of Record
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Published date: May 2017

Identifiers

Local EPrints ID: 415891
URI: https://eprints.soton.ac.uk/id/eprint/415891
PURE UUID: 2bb71e9b-ccd9-478b-a22d-41b770bd4ff4
ORCID for Wei Liu: ORCID iD orcid.org/0000-0002-4719-0345

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Date deposited: 28 Nov 2017 17:30
Last modified: 14 Mar 2019 01:54

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