Title :

OPTIMAL RATES FOR FINITE MIXTURE ESTIMATION

Author(s) :

Heinrich, Philippe [Auteur]
Laboratoire Paul Painlevé - UMR 8524 [LPP]
Kahn, Jonas [Auteur]
Laboratoire Paul Painlevé - UMR 8524 [LPP]

English keyword(s) :

strong identifiability.
rate of convergence
mixture model
mixing distribution
Wasserstein metric
maximum likelihood estimate
convergence of experiments
Local asymptotic normality
pointwise rate
Superefficient estimator

HAL domain(s) :

Mathématiques [math]/Statistiques [math.ST]

English abstract : [en]

We study the rates of estimation of finite mixing distributions, that is, the parameters of the mixture. We prove that under some regularity and strong identifiability conditions, around a given mixing distribution with ...
Show more >We study the rates of estimation of finite mixing distributions, that is, the parameters of the mixture. We prove that under some regularity and strong identifiability conditions, around a given mixing distribution with $m_0$ components, the optimal local minimax rate of estimation of a mixing distribution with $m$ components is $n^{-1/(4(m-m_0) + 2)}$. This corrects a previous paper by \citet{Chen} in The Annals ofStatistics.By contrast, it turns out that there are estimators with a(non-uniform) pointwise rate of estimation of $n^{-1/2}$ for all mixing distributions with a finite number of components.Show less >

Language :

Anglais

Comment :

48 pages, 1 figure, soumis à The Annals of Statistics en séparant l'article principal (30 pages) et les appendices (19 pages). «Minimax rates for finite mixtures», hal-01142343, ou arXiv:1504.03506, est une ancienne version, sans aucun résultat point par point, avec beaucoup moins de bibliographie et d'explications, et une présentation différente

Collections :

• Laboratoire Paul Painlevé - UMR 8524

Source :

Harvested from HAL