A Reformulation of Weighted Least Squares Estimators

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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.

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This document was originally published by The American Statistical Association in The American Statistician at http://pubs.amstat.org/doi/abs/10.1198/tast.2009.0011. Copyright restrictions may apply.