Stochastic EM

Publikation: Kapitel i bog/rapport/konferenceprocesEncyclopædiartikelForskning

Resumé

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.
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.
SprogEngelsk
TitelWiley StatsRef : Statistics Reference Online
RedaktørerMarie Davidian, Ron S. Kenett, Nicholas T. Longford, Geert Molenberghs, Walter Piegorsch, Fabrizio Ruggeri
Udgivelses stedHoboken, NJ
ForlagWiley
Dato15 maj 2018
ISBN (Elektronisk)9781118445112
DOI
StatusUdgivet - 15 maj 2018

Bibliografisk note

CBS Bibliotek har ikke adgang til materialet

Emneord

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

Citer dette

Nielsen, S. F. (2018). Stochastic EM. I M. Davidian, R. S. Kenett, N. T. Longford, G. Molenberghs, W. Piegorsch, & F. Ruggeri (red.), Wiley StatsRef: Statistics Reference Online Hoboken, NJ: Wiley. DOI: 10.1002/9781118445112.stat08121
Nielsen, Søren Feodor. / Stochastic EM. Wiley StatsRef: Statistics Reference Online. red. / Marie Davidian ; Ron S. Kenett ; Nicholas T. Longford ; Geert Molenberghs ; Walter Piegorsch ; Fabrizio Ruggeri. Hoboken, NJ : Wiley, 2018.
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Nielsen, SF 2018, Stochastic EM. i M Davidian, RS Kenett, NT Longford, G Molenberghs, W Piegorsch & F Ruggeri (red), Wiley StatsRef: Statistics Reference Online. Wiley, Hoboken, NJ. DOI: 10.1002/9781118445112.stat08121

Stochastic EM. / Nielsen, Søren Feodor.

Wiley StatsRef: Statistics Reference Online. red. / Marie Davidian; Ron S. Kenett; Nicholas T. Longford; Geert Molenberghs; Walter Piegorsch; Fabrizio Ruggeri. Hoboken, NJ : Wiley, 2018.

Publikation: Kapitel i bog/rapport/konferenceprocesEncyclopædiartikelForskning

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N2 - 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.

AB - 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.

KW - Incomplete data

KW - EM algorithm

KW - Imputation

KW - Simulation

KW - Estimation

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KW - EM algorithm

KW - Imputation

KW - Simulation

KW - Estimation

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Nielsen SF. Stochastic EM. I Davidian M, Kenett RS, Longford NT, Molenberghs G, Piegorsch W, Ruggeri F, red., Wiley StatsRef: Statistics Reference Online. Hoboken, NJ: Wiley. 2018. Tilgængelig fra, DOI: 10.1002/9781118445112.stat08121