Minimax rates for finite mixture estimation

Abstract

We prove that under some regularity and strong identifiability 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.

30 pages

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