Abstract
ABSTRACT Independent random samples are drawn from k( ≥ 2) normal populations having means Θ1,…, Θ k ; Θ1 ≤ Θ2 ≤ · · · ≤ Θ k and known variances . Estimation of Θ = (Θ1,…, Θ k ) with respect to the norm squared error loss is considered. Let δ p be the analog of the Pitman estimator of Θ, that is, the generalized Bayes estimator of Θ with respect to the uniform prior on the restricted space Ω = {Θ: Θ1 ≤ Θ2 ≤ · · · ≤ Θ k }. It has been proved earlier that when the ′s are equal, δ p is minimax. Here we exhibit for k = 3, that when ′s are unequal, the minimaxity of δ p may fail to hold. Furthermore, the risk performance of δ p is compared numerically with that of the restricted maximum likelihood estimator δ MLE and the usual estimator X = (X 1, X 2, X 3).
Published Version
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