CONSISTENCY OF A RECURSIVE ESTIMATE OF MIXING DISTRIBUTIONS

• 成果类型: Article
• 署名作者: Tokdar, Surya T.; Martin, Ryan; Ghosh, Jayanta K.
• 署名单位: Carnegie Mellon University; Purdue University System; Purdue University; Indian Statistical Institute; Indian Statistical Institute Kolkata
• 刊物名称: ANNALS OF STATISTICS
• ISSN/ISSBN: 0090-5364
• DOI: 10.1214/08-AOS639
• 发表日期: 2009
• 页码: 2502-2522
• 关键词: mixture model; posterior distributions; bayesian-analysis

摘要

Mixture models have received considerable attention recently and Newton [Sankhya Ser A 64 (2002) 306-322] proposed a fast recursive algorithm for estimating a mixing distribution. We prove almost sure consistency of this recursive estimate in the weak topology under mild conditions on the family of densities being mixed. This recursive estimate depends on the data ordering and a permutation-invariant modification is proposed, which is an average of the original over permutations of the data sequence. A Rao-Blackwell argument is used to prove consistency in probability of this alternative estimate. Several Simulations are presented, comparing the finite-sample performance of the recursive estimate and a Monte Carlo approximation to the permutation-invariant alternative along with that of the nonparametric maximum likelihood estimate and a nonparametric Bayes estimate.