Efficient maximum likelihood estimation in semiparametric mixture models. (English) Zbl 0860.62029
Summary: 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 \(\widehat {\theta}_n\) of the joint maximum likelihood estimator \((\widehat {\theta}_n, \widehat{\eta_n})\) is asymptotically normal and asymptotically efficient in the semiparametric sense.
MSC:
| 62F12 | Asymptotic properties of parametric estimators |
| 62G20 | Asymptotic properties of nonparametric inference |
| 62G05 | Nonparametric estimation |
Keywords:
asymptotic normality; Donsker class; asymptotic efficiency; efficient score equation; maximum likelihood estimation; semiparametric mixture models; exponential frailty model; errors-in-variables modelReferences:
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