Stochastic EM

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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
Publication date15 May 2018
ISBN (Electronic)9781118445112
Publication statusPublished - 15 May 2018


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

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