Geometric weighted least squares estimation - Oldenburg, Reinhard (Statistics, Optimization & Information Computing, 2024)
Optimal efficiency of least squares (LS) estimation requires that the error variables (residuals) have equal variance (homoscedasticity). In LS applications with multiple output variables, heteroscedasticity can even cause bias. In weighted LS, weights are chosen to compensate for differences in variance. The selection of these weights can be challenging, depending on the specific application. This paper introduces a general method, Geometric Weighted Least Squares (GWLS) estimation, which estimates weights using the inequality between the geometric and arithmetic means. A simulation study explores the performance of the method.