The GEM Algorithm

Nancy L. Glenn, Ph. D.
USC Department of Statistics
Columbia, SC


        The expectation maximization (EM) algorithm is a general iterative algorithm that employs parametric procedures for maximum likelihood estimation for missing data analysis. Since the EM algorithm uses parametric procedures, strong assumptions are made about the underlying distribution of the data. The GEM (Glenn EM) algorithm uses a nonparametric likelihood, empirical likelihood, for determining the maximum likelihood estimator in missing data problems. The GEM algorithm's advantage is that it makes few assumptions regarding the underlying distribution of the data. Using simulated data, a salinity data set, and the well{studied seed data found in Snedecor's 1956 paper, I show that the GEM algorithm provides convergence rates and estimation values that are comparable to those of the EM algorithm. I also investigate the GEM algorithm's robustness to initial estimates of starting values.