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Biometrika 1986 73(2):397-403; doi:10.1093/biomet/73.2.397
© 1986 by Biometrika Trust
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Likelihood methods for the discrimination problem

D. L. McLEISH and CHRISTOPHER G. SMALL

Department of Statistics and Actuarial Science, University of Waterloo Waterloo, Canada N2L 3G1

Suppose independent observations are drawn such that k have a known density g(x) and n – k have a known density f(x). We consider the discrimination problem of allocating observations to their parent densities. The rule minimizing the expected number of misclassifications is written as a function of k and estimators of k are investigated. Properties of the likelihood function of k based upon the order statistics are studied. We conclude that a mixture model analysis performs well regardless of the mechanism, stochastic or deterministic, which generates k and the correct allocation.

Key Words: Allocation • Discrimination • Likelihood • Mixture • Order Statistic


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