### Abstract

Some patterned covariance matrices used to model multivariate normal data that do not have explicit maximum likelihood estimates can be viewed as submatrices of larger patterned covariance matrices that do have explicit maximum likelihood estimates. In such cases, the smaller covariance matrix can be viewed as the covariance matrix for observed variables and the larger covariance matrix can be viewed as the covariance matrix for both observed and missing variables. The advantage of this perspective is that the em algorithm can be used to calculate the desired maximum likelihood estimates for the original problem. Two examples are presented.

Original language | English (US) |
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Pages (from-to) | 657-660 |

Number of pages | 4 |

Journal | Biometrika |

Volume | 69 |

Issue number | 3 |

DOIs | |

State | Published - Dec 1 1982 |

### All Science Journal Classification (ASJC) codes

- Statistics and Probability
- Mathematics(all)
- Agricultural and Biological Sciences (miscellaneous)
- Agricultural and Biological Sciences(all)
- Statistics, Probability and Uncertainty
- Applied Mathematics

### Keywords

- Circular symmetry
- EM algorithm
- Maximum likelihood
- Missing data
- Patterned covariance matrix
- Stationary covariance

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## Cite this

Rubin, D. B., & Szatrowski, T. H. (1982). Finding maximum likelihood estimates of patterned covariance matrices by the em algorithm.

*Biometrika*,*69*(3), 657-660. https://doi.org/10.1093/biomet/69.3.657