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April 1996 Efficient maximum likelihood estimation in semiparametric mixture models
Aad Van der Vaart
Ann. Statist. 24(2): 862-878 (April 1996). DOI: 10.1214/aos/1032894470


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.


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Aad Van der Vaart. "Efficient maximum likelihood estimation in semiparametric mixture models." Ann. Statist. 24 (2) 862 - 878, April 1996.


Published: April 1996
First available in Project Euclid: 24 September 2002

zbMATH: 0860.62029
MathSciNet: MR1394993
Digital Object Identifier: 10.1214/aos/1032894470

Primary: 62F12 , 62G20

Keywords: Asymptotic efficiency , Donsker class , efficient score equation , maximum likelihood , mixture model , Semiparametric model

Rights: Copyright © 1996 Institute of Mathematical Statistics

Vol.24 • No. 2 • April 1996
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