Bayes Discriminant Rules with Ordered Predictors |
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Authors: | Cristina Rueda Miguel A Fernández Bonifacio Salvador |
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Institution: | (1) Departamento de Estadística e I.O.Universidad de Valladolid, 47005 Valladolid, Spain |
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Abstract: | We propose and discuss improved Bayes rules to discriminate between two populations using ordered predictors. To address the
problem we propose an alternative formulation using a latent space that allows to introduce the information about the order
in the theoretical rules. The rules are first defined when the marginal densities are fully known and then under normality
when the parameters are unknown and training samples are available. Several numerical examples and simulations in the paper
illustrate the methodology and show that the new rules handle the information appropriately. We compare the new rules with
the classical Bayes and Fisher rules in these examples and we show that the misclassification probability is smaller for the
new rules. The method is also applied to data from a diabetes study where we again show that the new rules improve over the
usual Fisher rule.
Research partially supported by Spanish DGES and by PAPIJCL. The authors thank the editor and an anonymous reviewer for their
detailed reading that resulted in this much improved version of the paper. |
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Keywords: | Discriminant analysis Latent space Misclassification probability Order restrictions Restricted estimation |
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