Stochastic EM

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Abstract

The expectation maximization (EM) algorithm is a useful tool for finding the maximum likelihood estimator (MLE) in incomplete data problems. In some problems, however, the E step (and/or the M step) of the algorithm may be difficult to implement. Here, the stochastic EM algorithm can provide a useful alternative by replacing the E step of the EM algorithm with a fixed number of simulations, turning the M step into a maximization of the complete data log‐likelihood. The output of the stochastic EM algorithm forms a Markov chain that under sufficient regularity conditions is ergodic with an asymptotically normal invariant distribution. Draws from the invariant distribution form a consistent asymptotically normal estimator of the unknown parameters.
Original languageEnglish
Title of host publicationWiley StatsRef : Statistics Reference Online
EditorsMarie Davidian, Ron S. Kenett, Nicholas T. Longford, Geert Molenberghs, Walter Piegorsch, Fabrizio Ruggeri
Place of PublicationHoboken, NJ
PublisherWiley
Publication date15 May 2018
ISBN (Electronic)9781118445112
DOIs
Publication statusPublished - 15 May 2018

Bibliographical note

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Keywords

  • Incomplete data
  • EM algorithm
  • Imputation
  • Simulation
  • Estimation

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