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Optimal rates for finite mixture estimation

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arxiv 1507.04313 v1 pith:V7E3ERUN submitted 2015-07-15 math.ST stat.TH

classification math.STstat.TH
keywords estimationmixingcomponentsfinitedistributiondistributionsmixtureoptimal
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abstract

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 Chen (1995) in The Annals of Statistics. 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.

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Cited by 1 Pith paper

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Randomly initialized EM algorithm for two-component Gaussian mixture achieves near optimality in $O(\sqrt{n})$ iterations

    math.ST 2019-08 accept novelty 8.0 of 10

    Randomly initialized EM estimates the true center of a symmetric two-component Gaussian mixture to within logarithmic factors of the minimax rate in O(√n) iterations, given n=Ω(d log^3 d) samples.

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