Estimating the probabilities of misclassification in discriminant analysis

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1982
Authors
Ramos, Juan
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An observation assumed to have come from one of two populations, (PI)(,1) and (PI)(,2), is to be classified by the John's classification statistic Z. The unconditional probabilities of misclassification depend on the population parameters. When the parameters are unkown, these probabilities are also unknown and must be estimated from samples taken from the two populations;Several estimators for the unconditional probabilities of misclassification are considered. Some estimators are based on the assumption that the populations are normally distributed; other estimators do not require any distributional assumptions;Expressions for the asymptotic bias and asymptotic mean square error of each one of the estimators based on the normal distribution are obtained. These expressions are then used to compare the performance of the estimators;The uniformly minimum variance unbiased (UMVU) estimator of the expected value of Lachenbruch's leaving one-out estimator is obtained. The expected value of this UMVU estimator is used to obtain an exact expression for the unconditional probability of misclassification when the Z classification statistic is used;Finally, all estimators of the unconditional probabilities of misclassification are compared in a simulation study.

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