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.
Publié le : 1996-04-14
Classification:
Maximum likelihood,
semiparametric model,
mixture model,
Donsker class,
asymptotic efficiency,
efficient score equation,
62G20,
62F12
@article{1032894470,
author = {Van der Vaart, Aad},
title = {Efficient maximum likelihood estimation in semiparametric mixture models},
journal = {Ann. Statist.},
volume = {24},
number = {6},
year = {1996},
pages = { 862-878},
language = {en},
url = {http://dml.mathdoc.fr/item/1032894470}
}
Van der Vaart, Aad. Efficient maximum likelihood estimation in semiparametric mixture models. Ann. Statist., Tome 24 (1996) no. 6, pp. 862-878. http://gdmltest.u-ga.fr/item/1032894470/