#### Abstract

This paper presents and examines a new algorithm for solving a score equation for the maximum likelyhood estimate in certain problems of practical interest. The method circumvents the need to compute second order derivaties 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. Convergence properties of this fixed point algorithm are examined and asymptotics are derived for estimators obtained by using only a finite number of steps. Illustrative examples considered in the paper included bivariate and multivariate Gaussian copula models, nonnormal random effects and state space models. Properties of the algorithm and of estimators are evaluated in simulation studies on a bivariate copula model and a nonnormal linera random effects model.

#### Disciplines

Numerical Analysis and Computation | Statistical Methodology | Statistical Theory

#### Suggested Citation

Song, Peter Xuekun; Fan, Yanqin; and Kalbfleisch, Jack, "Maximization by Parts in Likelihood Inference" (June 2003). *The University of Michigan Department of Biostatistics Working Paper Series.* Working Paper 3.

http://biostats.bepress.com/umichbiostat/paper3

#### Included in

Numerical Analysis and Computation Commons, Statistical Methodology Commons, Statistical Theory Commons