On classical and other methods of discriminant analysis and estimation of log-odds

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dc.contributor.advisor Moran, M. A. en
dc.contributor.author Murphy, Brendan J.
dc.date.accessioned 2014-09-15T16:15:37Z
dc.date.available 2014-09-15T16:15:37Z
dc.date.issued 1981
dc.date.submitted 1981
dc.identifier.citation Murphy, B. J. 1981. On classical and other methods of discriminant analysis and estimation of log-odds. PhD Thesis, University College Cork. en
dc.identifier.uri http://hdl.handle.net/10468/1660
dc.description.abstract For two multinormal populations with equal covariance matrices the likelihood ratio discriminant function, an alternative allocation rule to the sample linear discriminant function when n1 ≠ n2 ,is studied analytically. With the assumption of a known covariance matrix its distribution is derived and the expectation of its actual and apparent error rates evaluated and compared with those of the sample linear discriminant function. This comparison indicates that the likelihood ratio allocation rule is robust to unequal sample sizes. The quadratic discriminant function is studied, its distribution reviewed and evaluation of its probabilities of misclassification discussed. For known covariance matrices the distribution of the sample quadratic discriminant function is derived. When the known covariance matrices are proportional exact expressions for the expectation of its actual and apparent error rates are obtained and evaluated. The effectiveness of the sample linear discriminant function for this case is also considered. Estimation of true log-odds for two multinormal populations with equal or unequal covariance matrices is studied. The estimative, Bayesian predictive and a kernel method are compared by evaluating their biases and mean square errors. Some algebraic expressions for these quantities are derived. With equal covariance matrices the predictive method is preferable. Where it derives this superiority is investigated by considering its performance for various levels of fixed true log-odds. It is also shown that the predictive method is sensitive to n1 ≠ n2. For unequal but proportional covariance matrices the unbiased estimative method is preferred. Product Normal kernel density estimates are used to give a kernel estimator of true log-odds. The effect of correlation in the variables with product kernels is considered. With equal covariance matrices the kernel and parametric estimators are compared by simulation. For moderately correlated variables and large dimension sizes the product kernel method is a good estimator of true log-odds. en
dc.format.mimetype application/pdf en
dc.language.iso en en
dc.publisher University College Cork en
dc.relation.uri http://library.ucc.ie/record=b1000044~S0
dc.rights © 1981, Brendan J. Murphy en
dc.rights.uri http://creativecommons.org/licenses/by-nc-nd/3.0/ en
dc.subject Multivariate analysis en
dc.subject.lcsh Discriminant analysis en
dc.title On classical and other methods of discriminant analysis and estimation of log-odds en
dc.type Doctoral thesis en
dc.type.qualificationlevel Doctoral en
dc.type.qualificationname PhD (Science) en
dc.internal.availability Full text available en
dc.check.info No embargo required en
dc.description.version Accepted Version
dc.description.status Not peer reviewed en
dc.internal.school Mathematics en
dc.check.type No Embargo Required
dc.check.reason No embargo required en
dc.check.opt-out Not applicable en
dc.thesis.opt-out false
dc.check.embargoformat Not applicable en
ucc.workflow.supervisor cora@ucc.ie


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© 1981, Brendan J. Murphy Except where otherwise noted, this item's license is described as © 1981, Brendan J. Murphy
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