Minimax rates for finite mixture estimation

Philippe Heinrich; Jonas Kahn

Minimax rates for finite mixture estimation

Statistics Theory 2015-04-15 v1 Statistics Theory

Authors: Philippe Heinrich , Jonas Kahn

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.

Cite

@article{arxiv.1504.03506,
  title  = {Minimax rates for finite mixture estimation},
  author = {Philippe Heinrich and Jonas Kahn},
  journal= {arXiv preprint arXiv:1504.03506},
  year   = {2015}
}

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30 pages

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