Characterizations of the best linear unbiased estimator in the general Gauss-Markov model with the use of matrix partial orderings
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Publication:910132
DOI10.1016/0024-3795(90)90349-HzbMath0695.62152MaRDI QIDQ910132
Jerzy K. Baksalary, Simo Puntanen
Publication date: 1990
Published in: Linear Algebra and its Applications (Search for Journal in Brave)
ordinary least squaresmatrix partial orderingsGauss-Markov modelLoewner orderingdispersion matrixbest linear unbiased estimatorsnew characterizations of BLUErank-subtractivity partial orderings
Related Items (13)
On connections among OLSEs and BLUEs of whole and partial parameters under a general linear model ⋮ Automorphisms of \(M_{n}\), partially ordered by rank subtractivity ordering ⋮ On the equality of estimators under a general partitioned linear model with parameter restrictions ⋮ Some further matrix extensions of the Cauchy-Schwarz and Kantorovich inequalities, with some statistical applications ⋮ The star partial order and the eigenprojection at 0 on EP matrices ⋮ On a partial order defined by the weighted Moore-Penrose inverse ⋮ THREE RANK FORMULAS ASSOCIATED WITH THE COVARIANCE MATRICES OF THE BLUE AND THE OLSE IN THE GENERAL LINEAR MODEL ⋮ Idempotent Boolean matrices and majorization ⋮ Matrix rank and inertia formulas in the analysis of general linear models ⋮ Solutions of minus partial ordering equations over von Neumann regular rings ⋮ Ordering of transformed recorded electroencephalography (EEG) signals by a novel precede operator ⋮ Ordered matrices with nonnegative group projector ⋮ Preservers of partial orders on the set of all variance-covariance matrices
Cites Work
- The matrix inequality \(M \leq B^*MB\)
- Inheriting independence and chi-squaredness under certain matrix orderings
- On some characterizations of the star partial ordering for matrices and rank subtractivity
- A relationship between the star and minus orderings
- The minus partial order and the shorted matrix
- An extension of a rank criterion for the least squares estimator to be the best linear unbiased estimator
- The rank of a difference of matrices and associated generalized inverses
- Characterizations of estimability in the general linear model
- Representations of best linear unbiased estimators in the Gauss-Markoff model with a singular dispersion matrix
- Some properties of matrix partial orderings
- Categorical information and the singular linear model
- Prior Information on the Coefficients when the Disturbance Covariance Matrix is Unknown
- On Canonical Forms, Non-Negative Covariance Matrices and Best and Simple Least Squares Linear Estimators in Linear Models
- Linear Spaces and Minimum Variance Unbiased Estimation
- Inequalities: theory of majorization and its applications
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