Efficient maximum likelihood estimation in semiparametric mixture models
The Annals of Statistics · 1996 · Volume 24 · Issue 2
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 $\int p_{\theta}(x|z) d \eta(z)$. The mixing distribution is completely unknown. We show that the first component $\hat{\theta}_n$ of the joint maximum likelihood estimator , $(\hat{\theta}_n \hat{\eta}_n)$ is asymptotically normal and asymptotically efficient in the semiparametric sense.
Keywords
62F12; 62G20; Asymptotic efficiency; Donsker class; efficient score equation; maximum likelihood; mixture model; Semiparametric model;
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