Geometric weighted least squares estimation
Keywords:
Weighted least squares, Geometric mean, Latent variables
Abstract
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.References
\bibitem{bollen}
\newblock K. Bollen,
\newblock \emph{Structural Equations with Latent Variables},
\newblock Wiley, 1989.
\bibitem{browne}
\newblock M. W. Browne,
\newblock \emph{ Asymptotically distribution-free methods for the analysis of covariance structures}, \newblock British Journal of Mathematical and Statistical Psychology, 37(1), pp. 62-83, 1984.
\bibitem{old1}
\newblock R. Oldenburg,
\newblock \emph{ Least square estimation of non-linear structural models},
\newblock Statistics, Optimization \& Information Computing, \textbf{12}, pp 281--297, 2024.
\bibitem{seber2003nonlinear}
\newblock G.A.F.Seber, and C. J. Wild,
\newblock \emph{ Nonlinear Regression},
\newblock Wiley, 2003.
\newblock K. Bollen,
\newblock \emph{Structural Equations with Latent Variables},
\newblock Wiley, 1989.
\bibitem{browne}
\newblock M. W. Browne,
\newblock \emph{ Asymptotically distribution-free methods for the analysis of covariance structures}, \newblock British Journal of Mathematical and Statistical Psychology, 37(1), pp. 62-83, 1984.
\bibitem{old1}
\newblock R. Oldenburg,
\newblock \emph{ Least square estimation of non-linear structural models},
\newblock Statistics, Optimization \& Information Computing, \textbf{12}, pp 281--297, 2024.
\bibitem{seber2003nonlinear}
\newblock G.A.F.Seber, and C. J. Wild,
\newblock \emph{ Nonlinear Regression},
\newblock Wiley, 2003.
Published
2024-12-19
How to Cite
Oldenburg, R. (2024). Geometric weighted least squares estimation. Statistics, Optimization & Information Computing. https://doi.org/10.19139/soic-2310-5070-2324
Issue
Section
Research Articles
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