# Asymptotic normality in mixture models

ESAIM: Probability and Statistics (2010)

- Volume: 1, page 17-33
- ISSN: 1292-8100

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topSara 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 -

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