Discrimination procedures, small sample performance
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Authors
Eaton, Thomas E.
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1963
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Monterey, CA; Naval Postgraduate School
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Abstract
The general two population discrimination problem is discussed briefly under various situations. Discrimination procedures using the linear discriminant function and a nonparametric procedure due to Ju L Hodges and E. Fix which classifies a random variable to a population on the basis of assigning it to the population which has the nearest observation to an observed value of the random variable are discussed and compared by computing the probabilities of misclassification for both procedures when the two populations are normal with equal covariance matrices. Probabilities of misclassification are computed for the nonparametric discriminator and the linear discriminant function for two small sample sizes for the case when the two populations being discriminated are exponential. In this latter case, both discrimination procedures are shown to give high probabilities of misclassification for certain values of the parameters of the distribution being discriminated. Regions are given in terms of the parameters of the two exponential distributions where one of the probabilities of error is greater than 0.5. A more complete investigation for larger sample sizes is recommended for the linear discriminant function and the nonparametric procedure discussed in this paper for the case when the two populations being discriminated are exponential.
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Thesis
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Mathematics and Mechanics
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Approved for public release; distribution is unlimited.
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This publication is a work of the U.S. Government as defined in Title 17, United States Code, Section 101. Copyright protection is not available for this work in the United States.