Original language | English |
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Title of host publication | Wiley StatsRef : Statistics Reference Online |

Editors | Marie Davidian, Ron S. Kenett, Nicholas T. Longford, Geert Molenberghs, Walter Piegorsch, Fabrizio Ruggeri |

Place of Publication | Hoboken, NJ |

Publisher | Wiley |

Publication date | 15 May 2018 |

ISBN (Electronic) | 9781118445112 |

DOIs | |

Publication status | Published - 15 May 2018 |

## 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.

### Bibliographical note

CBS Library does not have access to the material## Keywords

- Incomplete data
- EM algorithm
- Imputation
- Simulation
- Estimation