When are Gauss-Markov and Least Squares Estimators Identical? A Coordinate-Free Approach
From MaRDI portal
Publication:5544768
DOI10.1214/aoms/1177698505zbMath0162.21902OpenAlexW1988407346WikidataQ30053850 ScholiaQ30053850MaRDI QIDQ5544768
Publication date: 1968
Published in: The Annals of Mathematical Statistics (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1214/aoms/1177698505
Related Items (63)
On connections among OLSEs and BLUEs of whole and partial parameters under a general linear model ⋮ Computation of the GLS estimator of a model with anticipated and unanticipated effects ⋮ The linear model with variance-covariance components and jackknife estimation ⋮ When are two step estimators efficient? ⋮ On the equality of estimators under a general partitioned linear model with parameter restrictions ⋮ Unnamed Item ⋮ Consistency of the least squares and Gauss-Markov estimators in regression models ⋮ Determinant formulas with applications to designing when the observations are correlated ⋮ Comparing the BLUEs Under Two Linear Models ⋮ Consistency of the least squares and Gauss-Markov estimators in regression models ⋮ On the notion of orthogonal projection in a semi-Euclidean space ⋮ Concentration Ellipsoids, Their Planes of Support, and the Linear Regression Model ⋮ Asymptotic efficiency of the ordinary least-squares estimator for SUR models with integrated regressors ⋮ On equalities of estimations of parametric functions under a general linear model and its restricted models ⋮ A note on the inefficiency of non-linear estimators ⋮ Best unbiased estimates for parameters of three-level multivariate data with doubly exchangeable covariance structure ⋮ Let us do the twist again ⋮ From equivalent linear equations to Gauss-Markov theorem ⋮ Partial GLS regression ⋮ A final twist on the equality of OLS and GLS ⋮ A unified approach to coordinate-free multivariate analysis ⋮ A note on the Gauss-Markov theorem ⋮ Optimal estimation for doubly multivariate data in blocked compound symmetric covariance structure ⋮ When is the pseudo-best estimator BLUE? ⋮ The Algebra of Estimation in Linear Econometric Systems∗ ⋮ Quadratic estimators of covariance components in a multivariate mixed linear model ⋮ Optimal design for linear models with correlated observations ⋮ Estimation of means in graphical Gaussian models with symmetries ⋮ The William Kruskal legacy: 1919-2005 ⋮ William H. Kruskal and the development of coordinate-free methods ⋮ On the existence of the Gauss-Markov estimators in linear mixed models ⋮ Admissible linear estimators in mixed linear models ⋮ Characterization of invariant spaces under a symmetric real matrix and its permutations ⋮ On the equivalence of the weighted least squares and the generalised least squares estimators, with applications to kernel smoothing ⋮ The frisch-waugh theorem and generalized least squares ⋮ EFFICIENT ESTIMATION OF FACTOR MODELS ⋮ Asymptotic efficiency of the OLSE for polynomial regression models with spatially correlated errors ⋮ Free-coordinate estimation for doubly multivariate data ⋮ Recursive estimation and generated regressors ⋮ Matrix rank and inertia formulas in the analysis of general linear models ⋮ Perfect linear models and perfect parametric functions ⋮ On D-optimal designs for linear models under correlated observations with an application to a linear model with multiple response ⋮ Properties of ordinary least squares estimators in regression models with nonspherical disturbances ⋮ On exact \(D\)-optimal designs for regression models with correlated observations ⋮ Conditions for the numerical equality of the OLS, GLS and Amemiya-Cragg estimators ⋮ All about the \(\bot\) with its applications in the linear statistical models ⋮ Evaluation of Measurement Comparisons Using Generalized Least Squares: the Role of Participants’ Estimates of Systematic Error ⋮ The equality of OLS and GLS estimators in the linear regression model when the disturbances are spatially correlated ⋮ A Jackknife Method for Estimation of Variance Components ⋮ Estimability of variance components when all model matrices commute ⋮ Weighted Generalized Inverses, Oblique Projections, and Least-Squares Problems ⋮ The sensitivity of OLS when the variance matrix is (partially) unknown ⋮ Efficiency of the OLSE for regressions on two-dimensional grids with sinusoidal regressors and spatially correlated errors ⋮ Testing and estimation of equal variances for correlated variables ⋮ REDUNDANCY OF MOMENT CONDITIONS AND THE EFFICIENCY OF OLS IN SUR MODELS ⋮ Another twist on the equality of OLS and GLS ⋮ A generalization of Rao's covariance structure with applications to several linear models ⋮ Unnamed Item ⋮ Sufficent conditions for orthogonal designs in mixed linear models ⋮ On the quality of likelihood-based estimators in spatial autoregressive models when the data dependence structure is misspecified ⋮ Unnamed Item ⋮ Lower bound of risk in linear unbiased estimation and its application ⋮ Mean driven balance and uniformly best linear unbiased estimators
This page was built for publication: When are Gauss-Markov and Least Squares Estimators Identical? A Coordinate-Free Approach
