### Abstract

This article presents and examines a new algorithm for solving a score equation for the maximum likelihood estimate in certain problems of practical interest. The method circumvents the need to compute second-order derivatives of the full likelihood function. It exploits the structure of certain models that yield a natural decomposition of a very complicated likelihood function. In this decomposition, the first part is a log-likelihood from a simply analyzed model, and the second part is used to update estimates from the first part. Convergence properties of this iterative (fixed-point) algorithm are examined, and asymptotics are derived for estimators obtained using only a finite number of iterations. Illustrative examples considered in the article include multivariate Gaussian copula models, nonnormal random-effects models, generalized linear mixed models, and state-space models. Properties of the algorithm and of estimators are evaluated in simulation studies on a bivariate copula model and a nonnormal linear random-effects model.

Original language | English (US) |
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Pages (from-to) | 1145-1158 |

Number of pages | 14 |

Journal | Journal of the American Statistical Association |

Volume | 100 |

Issue number | 472 |

DOIs | |

State | Published - Dec 2005 |

### Keywords

- Copula model
- Fixed-point algorithm
- Generalized linear mixed model
- Information dominance
- Iterative algorithm
- Non-normal random effects
- Score equation
- State-space model

### ASJC Scopus subject areas

- Statistics and Probability
- Statistics, Probability and Uncertainty

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## Cite this

*Journal of the American Statistical Association*,

*100*(472), 1145-1158. https://doi.org/10.1198/016214505000000204