ASYMPTOTICALLY EFFICIENT ESTIMATION OF PRIOR PROBABILITIES IN MULTICLASS FINITE MIXTURES

Efficient estimators for mixing probabilities in finite class mixtures are not realizable. Earlier published work on this topic has merely conjectured that asymptotically efficient estimators are realizable. We synthesize a prior probability estimator, a candidate for asymptotic efficiency, from within the class of recursive estimators proposed in our earlier work [2]. We prove asymptotic efficiency and convergence with probability one by involving a stochastic approximation theorem. The estimator can be implemented in practice for continuous, discrete, and mixed class conditional density functions, although continuous and mixed densities generally require repeated evaluation of expectations of certain functions through numerical techniques. Results of a simulation experiment with discrete densities are included. Variations of the estimator, for computational simplicity, are discussed.