2015/09/24 by Hua Zhou, Liuyi Hu, Zhou, Hua +5 · 1 citation
Computer Science · Mathematics · #60K05 #62J02 #90C30 #Bayesian Methods and Mixture Models #Computation (stat.CO) #FOS: Computer and information sciences #Methodology (stat.ME) #Statistical Methods and Bayesian Inference #Statistical Methods and Inference
paper · pdf · doi:10.48550/arxiv.1509.07426
openalex publication_date 2015/09/24 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Variance components estimation and mixed model analysis are central themes in statistics with applications in numerous scientific disciplines. Despite the best efforts of generations of statisticians and numerical analysts, maximum likelihood estimation and restricted maximum likelihood estimation of variance component models remain numerically challenging. Building on the minorization-maximization (MM) principle, this paper presents a novel iterative algorithm for variance components estimation. MM algorithm is trivial to implement and competitive on large data problems. The algorithm readily extends to more complicated problems such as linear mixed models, multivariate response models possibly with missing data, maximum a posteriori estimation, penalized estimation, and generalized estimating equations (GEE). We establish the global convergence of the MM algorithm to a KKT point and demonstrate, both numerically and theoretically, that it converges faster than the classical EM algorithm when the number of variance components is greater than two and all covariance matrices are positive definite.