2009/07/15 by Surya T. Tokdar, Ryan Martin, Jayanta K. Ghosh · 1 citation
Computer Science · Mathematics · #Bayesian Methods and Mixture Models #Statistical Methods and Inference #Statistical Methods in Clinical Trials #math.ST #msc:62G05 #msc:62G07 #msc:62L20 #stat.TH
paper · pdf · doi:10.1214/08-aos639
published as Annals of Statistics 2009, Vol. 37, No. 5A, 2502-2522 · Published in at http://dx.doi.org/10.1214/08-AOS639 the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org)
openalex publication_date 2009/07/15 · arxiv created 2009/08/24 · arxiv updated 2009/12/01 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28
Mixture models have received considerable attention recently and Newton [Sankhyā 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.