The Annals of Statistics

Efficient maximum likelihood estimation in semiparametric mixture models

Aad Van der Vaart

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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.

Article information

Source
Ann. Statist., Volume 24, Number 2 (1996), 862-878.

Dates
First available in Project Euclid: 24 September 2002

Permanent link to this document
https://projecteuclid.org/euclid.aos/1032894470

Digital Object Identifier
doi:10.1214/aos/1032894470

Mathematical Reviews number (MathSciNet)
MR1394993

Zentralblatt MATH identifier
0860.62029

Subjects
Primary: 62G20: Asymptotic properties 62F12: Asymptotic properties of estimators

Keywords
Maximum likelihood semiparametric model mixture model Donsker class asymptotic efficiency efficient score equation

Citation

Van der Vaart, Aad. Efficient maximum likelihood estimation in semiparametric mixture models. Ann. Statist. 24 (1996), no. 2, 862--878. doi:10.1214/aos/1032894470. https://projecteuclid.org/euclid.aos/1032894470


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