Seminario - From Closed-Form Estimation to EM-Type Algorithms

Abstract: Statistical estimation often relies on repeated numerical optimization, which can become costly in complex models. This talk presents a formal construction of closed-form estimators through model-derived estimating equations, examining their relationship with maximum likelihood, consistency, asymptotic normality, and standard-error estimation. Particular attention is given to the conditions under which explicit solutions exist and how their statistical properties can be established. We then extend these ideas to latent-variable models by taking conditional expectations of complete-data estimating equations, leading to explicit updates within EM-type algorithms. When a global closed-form solution is unavailable, local score-based constructions avoid fully solving a nonlinear optimization problem at each iteration while retaining the likelihood stationary equation. Nonlinear mixed-effects models, quantile regression with random effects, and hidden Markov models illustrate the approach. Simulation results and an application to growth curves highlight the computational gains, the settings in which they arise, and their implications for convergence and statistical inference.