Open Access
October 2009 Consistency of a recursive estimate of mixing distributions
Surya T. Tokdar, Ryan Martin, Jayanta K. Ghosh
Ann. Statist. 37(5A): 2502-2522 (October 2009). DOI: 10.1214/08-AOS639


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.


Download Citation

Surya T. Tokdar. Ryan Martin. Jayanta K. Ghosh. "Consistency of a recursive estimate of mixing distributions." Ann. Statist. 37 (5A) 2502 - 2522, October 2009.


Published: October 2009
First available in Project Euclid: 15 July 2009

zbMATH: 1173.62020
MathSciNet: MR2543700
Digital Object Identifier: 10.1214/08-AOS639

Primary: 62G07
Secondary: 62G05 , 62L20

Keywords: Empirical Bayes , Mixture models , recursive density estimation

Rights: Copyright © 2009 Institute of Mathematical Statistics

Vol.37 • No. 5A • October 2009
Back to Top