Consistency of a recursive estimate of mixingdistributions

Journal Article (Journal Article)

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. © Institute of Mathematical Statistics, 2009.

Full Text

Duke Authors

Cited Authors

  • Tokdar, ST; Ryan, M; Ghosh, JK

Published Date

  • October 1, 2009

Published In

Volume / Issue

  • 37 / 5 A

Start / End Page

  • 2502 - 2522

International Standard Serial Number (ISSN)

  • 0090-5364

Digital Object Identifier (DOI)

  • 10.1214/08-AOS639

Citation Source

  • Scopus