Efficient maximum likelihood estimation in semiparametric mixture models

Abstract

We consider maximum likelihood estimation in several examples of semiparametric mixture models, including the exponential frailty model and the errors-in-variables model. The observations consist of a sample of size n from the mixture density ∫pθ(x|z) dη(z). The mixing distribution is completely unknown. We show that the first component θ̂n of the joint maximum likelihood estimator (θ̂n, η̂n) is asymptotically normal and asymptotically efficient in the semiparametric sense.