STRONG IDENTIFIABILITY AND OPTIMAL MINIMAX RATES FOR FINITE MIXTURE ESTIMATION

• 成果类型: Article
• 署名作者: Heinrich, Philippe; Kahn, Jonas
• 署名单位: Universite de Lille; Universite de Toulouse; Universite Toulouse III - Paul Sabatier
• 刊物名称: ANNALS OF STATISTICS
• ISSN/ISSBN: 0090-5364
• DOI: 10.1214/17-AOS1641
• 发表日期: 2018
• 页码: 2844-2870
• 关键词: parameter-estimation; convergence-rates; deconvolution; ORDER

摘要

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-m0)+2)). This corrects a previous paper by Chen [Ann. Statist. 23 (1995) 221-233]. By contrast, it turns out that there are estimators with a (nonuniform) pointwise rate of estimation of n(-1/2) for all mixing distributions with a finite number of components.