# Testing in locally conic models, and application to mixture models

Didier Dacunha-Castelle; Elisabeth Gassiat

ESAIM: Probability and Statistics (2010)

- Volume: 1, page 285-317
- ISSN: 1292-8100

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topDacunha-Castelle, Didier, and Gassiat, Elisabeth. "Testing in locally conic models, and application to mixture models." ESAIM: Probability and Statistics 1 (2010): 285-317. <http://eudml.org/doc/116581>.

@article{Dacunha2010,

abstract = {
In this paper, we address the problem of testing hypotheses
using maximum likelihood statistics in non identifiable models.
We derive the asymptotic distribution under very general assumptions.
The key idea is a local reparameterization, depending on the underlying
distribution, which is called locally conic. This method enlights how
the general model induces the structure of the limiting distribution
in terms of dimensionality of some derivative space. We present various
applications of the theory. The main application is to mixture models.
Under very general assumptions, we solve completely the problem
of testing the size of the mixture using maximum likelihood statistics.
We derive the asymptotic distribution of the maximum likelihood statistic
ratio which takes an unexpected form.
},

author = {Dacunha-Castelle, Didier, Gassiat, Elisabeth},

journal = {ESAIM: Probability and Statistics},

keywords = {Likelihood tests / mixture models / locally conic models /
non identifiable models. },

language = {eng},

month = {3},

pages = {285-317},

publisher = {EDP Sciences},

title = {Testing in locally conic models, and application to mixture models},

url = {http://eudml.org/doc/116581},

volume = {1},

year = {2010},

}

TY - JOUR

AU - Dacunha-Castelle, Didier

AU - Gassiat, Elisabeth

TI - Testing in locally conic models, and application to mixture models

JO - ESAIM: Probability and Statistics

DA - 2010/3//

PB - EDP Sciences

VL - 1

SP - 285

EP - 317

AB -
In this paper, we address the problem of testing hypotheses
using maximum likelihood statistics in non identifiable models.
We derive the asymptotic distribution under very general assumptions.
The key idea is a local reparameterization, depending on the underlying
distribution, which is called locally conic. This method enlights how
the general model induces the structure of the limiting distribution
in terms of dimensionality of some derivative space. We present various
applications of the theory. The main application is to mixture models.
Under very general assumptions, we solve completely the problem
of testing the size of the mixture using maximum likelihood statistics.
We derive the asymptotic distribution of the maximum likelihood statistic
ratio which takes an unexpected form.

LA - eng

KW - Likelihood tests / mixture models / locally conic models /
non identifiable models.

UR - http://eudml.org/doc/116581

ER -

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