A Reformulation of Weighted Least Squares Estimators
This article studies weighted, generalized, least squares estimators in simple linear regression with serially correlated errors. Closed-form expressions of weighted least squares estimators and variances are presented under some common stationary autocorrelation settings, a first-order autoregression and a first-order moving-average. These explicit expressions also have appealing applications, including an efficient weighted least squares computation method and a new sufficient and necessary condition on the equality of weighted least squares estimators and ordinary least squares estimators.
Lee, Jaechoul. (2009). "A Reformulation of Weighted Least Squares Estimators". The American Statistician, 63(1), 49-55. http://dx.doi.org/10.1198/tast.2009.0011