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April, 1971 Linear Spaces and Minimum Variance Unbiased Estimation
Justus Seely, George Zyskind
Ann. Math. Statist. 42(2): 691-703 (April, 1971). DOI: 10.1214/aoms/1177693418


Consideration is given to minimum variance unbiased estimation when the choice of estimators is restricted to a finite-dimensional linear space. The discussion gives generalizations and minor extensions of known results in linear model theory utilizing both the coordinate-free approach of Kruskal and the usual parametric representations. Included are (i) a restatement of a theorem on minimum variance unbiased estimation by Lehmann and Scheffe; (ii) a minor extension of a theorem by Zyskind on best linear unbiased estimation; (iii) a generalization of the covariance adjustment procedure described by Rao; (iv) a generalization of the normal equations; and (v) criteria for existence of minimum variance unbiased estimators by means of invariant subspaces. Illustrative examples are included.


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Justus Seely. George Zyskind. "Linear Spaces and Minimum Variance Unbiased Estimation." Ann. Math. Statist. 42 (2) 691 - 703, April, 1971.


Published: April, 1971
First available in Project Euclid: 27 April 2007

zbMATH: 0217.51602
MathSciNet: MR292232
Digital Object Identifier: 10.1214/aoms/1177693418

Rights: Copyright © 1971 Institute of Mathematical Statistics

Vol.42 • No. 2 • April, 1971
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