Year: 2015
Type: preprint
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.
Source: arXiv (Cornell University)
Authors: Heinrich, Philippe, Kahn, Jonas
Institution: Laboratoire Paul Painlevé
Language: English
Subfield: Artificial Intelligence
Field: Computer Science
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W4289866619