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Likelihood methods for the discrimination problem. (English) Zbl 0632.62057

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.

MSC:

62H30 Classification and discrimination; cluster analysis (statistical aspects)
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