Strong identifiability and optimal minimax rates for finite mixture estimation

Philippe Heinrich (1) , Jonas Kahn (1)

1 LPP - Laboratoire Paul Painlevé - UMR 8524

We prove that under some regularity and strong iden-tifiability conditions, around a mixing distribution with $m_0$ components, the optimal local minimax rate of estimation of a mixture with $m$ components is $n^{−1/(4(m−m 0)+2)}$. This corrects a previous paper by Chen (1995) in The Annals of Statistics.

Mots clés: strong identifiability.; rate of convergence; mixture model; mixing distribution; Wasserstein metric; maximum likelihood estimate; convergence of experiments; Local asymptotic normality

Domaines: Statistiques [math.ST]

Philippe Heinrich, Jonas Kahn. Strong identifiability and optimal minimax rates for finite mixture estimation. Annals of Statistics, 2018, 46 (6A), pp.2844-2870. ⟨hal-01142343v2⟩