Asymptotic normality in mixture models

Sara Van De Geer. "Asymptotic normality in mixture models." ESAIM: Probability and Statistics 1 (2010): 17-33. <http://eudml.org/doc/197751>.

@article{SaraVanDeGeer2010,
abstract = { We study the estimation of a linear integral functional of a distribution F, using i.i.d. observations which density is a mixture of a family of densities k(.,y) under F. We examine the asymptotic distribution of the estimator obtained by plugging the non parametric maximum likelihood estimator (NPMLE) of F in the functional. A problem here is that usually, the NPMLE does not dominate F.
Our main aim here is to show that this can be overcome by considering a convex combination of F and the NPMLE. },
author = {Sara Van De Geer},
journal = {ESAIM: Probability and Statistics},
keywords = {Asymptotic efficiency / asymptotic normality / differentiable functionals / maximum likelihood / mixture model.; Asymptotic efficiency; asymptotic normality; differentiable functionals; linear integral functional; mixture model; nonparametric maximum likelihood estimator; NPMLE},
language = {eng},
month = {3},
pages = {17-33},
publisher = {EDP Sciences},
title = {Asymptotic normality in mixture models},
url = {http://eudml.org/doc/197751},
volume = {1},
year = {2010},
}

TY - JOUR
AU - Sara Van De Geer
TI - Asymptotic normality in mixture models
JO - ESAIM: Probability and Statistics
DA - 2010/3//
PB - EDP Sciences
VL - 1
SP - 17
EP - 33
AB - We study the estimation of a linear integral functional of a distribution F, using i.i.d. observations which density is a mixture of a family of densities k(.,y) under F. We examine the asymptotic distribution of the estimator obtained by plugging the non parametric maximum likelihood estimator (NPMLE) of F in the functional. A problem here is that usually, the NPMLE does not dominate F.
Our main aim here is to show that this can be overcome by considering a convex combination of F and the NPMLE.
LA - eng
KW - Asymptotic efficiency / asymptotic normality / differentiable functionals / maximum likelihood / mixture model.; Asymptotic efficiency; asymptotic normality; differentiable functionals; linear integral functional; mixture model; nonparametric maximum likelihood estimator; NPMLE
UR - http://eudml.org/doc/197751
ER -