CONSISTENCY OF A RECURSIVE ESTIMATE OF MIXING DISTRIBUTIONS

By Surya T. Tokdar, Ryan Martin, Jayanta Kumar Ghosh. 2009

65 citations recorded by the source corpus.

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.

Subfields: Artificial Intelligence, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/429f260a3021a1d1b35a23fc4809263611b82b1e

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Citations in the corpus

Fast Bayesian Inference in Dirichlet Process Mixture Models (2011, methodology): “Because π n depends on the ordering of (y 1 ,... ,y n ) , following the recommendation of Newton (2002) and Tokdar, Martin, and Ghosh (2009), we use the average of f n (y) over 10 permutations.”
Martingale posterior distributions (2021, methodology): “Theoretical properties of permutation averaging are explored in Tokdar et al. (2009); Dixit and Martin (2019), which we do not consider here.”