Maximum Likelihood Estimation from Incomplete Data via EM-Type Algorithms

This article reviews EM-type algorithms, including the Expectation- Maximization (EM), Expectation-Conditional-Maximization (ECM), Expectation-Conditional-Maximization-Either (ECME), and Parameter- Expanded-Expectation-Maximization (PX-EM) algorithms, which are popular tools for modal estimation from incomplete data. These algorithms are presented along with maximum likelihood estimation of the t-distribution, which has played an important role in the development of EM-type algorithms and robust estimation. Existing algorithms are reviewed and new algorithms are proposed for maximum likelihood estimation of the general linear mixed-effects models, which has become a popular tool for analyzing repeated measures and longitudinal data in many fields such as biology and medicine.