Original language | English |
---|---|

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

### Bibliographical note

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

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

### Cite this

*Wiley StatsRef: Statistics Reference Online*Hoboken, NJ: Wiley. https://doi.org/10.1002/9781118445112.stat08121

}

*Wiley StatsRef: Statistics Reference Online.*Wiley, Hoboken, NJ. https://doi.org/10.1002/9781118445112.stat08121

**Stochastic EM.** / Nielsen, Søren Feodor.

Research output: Chapter in Book/Report/Conference proceeding › Encyclopedia chapter › Research

TY - ENCYC

T1 - Stochastic EM

AU - Nielsen, Søren Feodor

N1 - CBS Library does not have access to the material

PY - 2018/5/15

Y1 - 2018/5/15

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

KW - Incomplete data

KW - EM algorithm

KW - Imputation

KW - Simulation

KW - Estimation

U2 - 10.1002/9781118445112.stat08121

DO - 10.1002/9781118445112.stat08121

M3 - Encyclopedia chapter

BT - Wiley StatsRef

A2 - Davidian, Marie

A2 - Kenett, Ron S.

A2 - Longford, Nicholas T.

A2 - Molenberghs, Geert

A2 - Piegorsch, Walter

A2 - Ruggeri, Fabrizio

PB - Wiley

CY - Hoboken, NJ

ER -