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June, 1983 Estimation Via Linearly Combining Two Given Statistics
J. K. Baksalary, R. Kala
Ann. Statist. 11(2): 691-696 (June, 1983). DOI: 10.1214/aos/1176346173


We consider the problems of (i) covariance adjustment of an unbiased estimator, (ii) combining two unbiased estimators, and (iii) improving upon an unbiased estimator. All these problems consist in determining a minimum dispersion linear unbiased combination of given two statistics, one of which is an unbiased estimator of a vector parameter $\mathbf{\theta} \in \mathscr{H}$, and the expectation of the other is a zero vector in the problem of covariance adjustment, is equal to $\mathbf{\theta}$ in the problem of combining, and is equal to a subvector of $\mathbf{\theta}$ in the problem of improving. The solutions obtained are substantial generalizations of known results, in the sense that they are valid for an arbitrary joint dispersion matrix of the given statistics as well as for the parameter space $\mathscr{H}$ being an arbitrary subspace of $\mathscr{R}^k$.


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J. K. Baksalary. R. Kala. "Estimation Via Linearly Combining Two Given Statistics." Ann. Statist. 11 (2) 691 - 696, June, 1983.


Published: June, 1983
First available in Project Euclid: 12 April 2007

zbMATH: 0515.62053
MathSciNet: MR696079
Digital Object Identifier: 10.1214/aos/1176346173

Primary: 62F10
Secondary: 62J99

Keywords: combining two unbiased estimators , Covariance adjustment of an unbiased estimator , improving upon an unbiased estimator

Rights: Copyright © 1983 Institute of Mathematical Statistics


Vol.11 • No. 2 • June, 1983
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