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- W629765140 abstract "We have seen that the computation of a general minimax strategy with regard to the parameter space $$otimes = left{ {theta in mathbb{R}^N :sumlimits_text{i} {frac{1} {{text{p}_text{i} }}} (text{y}_text{i} text{ - p}_text{i} text{y})^2 leqslant text{c}^2 } right}$$ with c>0 in nD1 or in nD u1 often is not feasible. The classical minimax criterion as an optimal decision rule appears to be too unmanageable to get feasible solutions. This fact changes at once if we are interested not only in the maximum of the risk on ⊗ but also in the other extrema of the risk on ⊗, as indicated in 1.8. The conditional minimax approach of 1.9 is another way of obtaining feasible solutions. Mathematically both approaches lead to similar results and can be treated together. Without difficulty we can generalize the parameter space to the generalized HH- space $$otimes = left{ {theta in mathbb{R}^N :theta 'Vtheta leqslant text{c}^text{2} } right}$$ where V is a nonnegative definite symmetric matrix of rank N- H, and VQ=0, Q a N×H matrix of rank H. For H=1 the HH- space is an example of such a ⊗. We set V = diag(1/p1,…1/pN) — ee’, where e = (1,…1)’, and Q=(p1,…pN)’.KeywordsParameter SpaceLinear EstimatorRegular MatrixOptimal Decision RuleMinimax EstimatorThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves." @default.
- W629765140 created "2016-06-24" @default.
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- W629765140 date "1990-01-01" @default.
- W629765140 modified "2023-09-25" @default.
- W629765140 title "The Generalized HH- Space as Parameter Space" @default.
- W629765140 doi "https://doi.org/10.1007/978-1-4612-3442-5_5" @default.
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