Bias associated with the discriminant analysis approach to the estimation of mixing proportions

The estimation of the mixing proportion π₁, in which the first of two multivariate normal groups occur is considered on the basis of a sample drawn from a mixture of them. Under the model studied, there are also data of known origin available from each of the groups for the formation of a discriminant rule R. The bias of the estimator of π₁, based on the proportion of the mixture data assigned to the first group by R, is investigated. Also, the case where the data of known origin are taken to be correlated is considered.