Fast, closed-form, and efficient estimators for hierarchical models with AR(1) covariance and unequal cluster sizes

This article is concerned with statistically and computationally efficient estimation in a hierarchical data setting with unequal cluster sizes and an AR(1) covariance structure. Maximum likelihood estimation for AR(1) requires numerical iteration when cluster sizes are unequal. A near optimal non-iterative procedure is proposed. Pseudo-likelihood and split-sample methods are used, resulting in computing weights to combine cluster size specific parameter estimates. Results show that the method is statistically nearly as efficient as maximum likelihood, but shows great savings in computation time.