Likelihood methods for the discrimination problem
Don L. McLeish, Christopher G. Small · Biometrika · 1986
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.