Linear experiments, stochastic ordering, comparison of experiments, S-convex functions, l-way random model,

Let Y be observable random vector such that EY=Xβ and D(Y)=ρ2V. Linear estimation of a parameter p′β under the squared loss is considered. RAO, 1976 and 1979, obtained a necessary and sufficient condition for admissibility of an estimator t′Y in the case X=I. This result will be extended for arbitrary X. AMS 1970 subject classifications. Primary 62J05; secondary 62C15.

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SummaryIt is shown that in linear estimation, both unbiased and biased, all unique (up to equivalence with respect to risk) locally best estimators and their limits constitute a complete class.

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