Strong identifiability and optimal minimax rates for finite mixture estimation - Archive ouverte HAL
Journal Articles Annals of Statistics Year : 2018

Strong identifiability and optimal minimax rates for finite mixture estimation

Jonas Kahn

Abstract

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.
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Dates and versions

hal-01142343 , version 1 (15-04-2015)
hal-01142343 , version 2 (19-12-2018)

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Cite

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⟩
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