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Minimax linear regression estimation with symmetric parameter restrictions. (English) Zbl 0602.62054
The author considers a linear regression model \(E(y)=X\cdot \theta\), \(\theta\in \Theta\), cov y\(=W\) (W assumed to be positive definite) with restricted parameter space \(\Theta \subset R^ K\), where \(\Theta\) is compact and symmetric about some centre point \(\theta_ 0\in R^ K\). This includes, as special cases, ellipsoid constraints \((\theta - \theta_ 0)'H(\theta -\theta_ 0)\leq 1\) with a positive definite matrix H and linear constraints. The explicit form of the minimax linear estimator involves the second moment matrix of a least favourable prior distribution on \(\Theta\). Explicit minimax linear estimators are determined for the important special cases of the above inequality.
Reviewer: J.Kaufmann

MSC:
62J05 Linear regression; mixed models
62F15 Bayesian inference
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