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arXiv · 1507.04313

Optimal rates for finite mixture estimation

Philippe Heinrich·Jonas Kahn
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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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Philippe Heinrich, Jonas Kahn. 2015-07-15. Optimal rates for finite mixture estimation. https://arxiv.org/abs/1507.04313

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