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The admissibility of Pitman’s estimator of a single location parameter. Ann. Math. , 30, 970–979. MR109392 [27] Zidek, J. V. (1970). Sufficient conditions for admissibility under squared error loss of formal Bayes estimators. Ann. Math. Statist. 41, 446–456. MR261742 A Festschrift for Herman Rubin Institute of Mathematical Statistics Lecture Notes – Monograph Series Vol. 45 (2004) 21–44 c Institute of Mathematical Statistics, 2004 Estimation in restricted parameter spaces: A review Eric Marchand∗1 and William E.

So that R(dwi+1 |wi ) is the conditional distribution of Wi+1 given Wi = wi , for i = 0, 1, 2, . .. The unique probability measure on path space that is consistent with this Markov specification, is denoted by S(·|w0 ). Because the space Y is rather general, the definition of recurrence has to be selected with some care. The reader should note that neither irreducibility nor periodicity occur in the discussion that follows (see Meyn and Tweedie (1993) for a discussion of such things in the general state space case).

In Theorem 2, it is worth pointing out, and it follows immediately that Gh (y, θ) ≤ 0, for all y, with equality iff h = hU and θ = 0, which indicates that, for the dominating estimators of Theorem 2, R(θ, δh (X)) ≤ R(θ, δ0 (X)) with equality iff h = hU and θ = 0. 4 for a discussion on a normal model δ + (X)). 2. Some related results to Theorem 2 For general location family densities f0 (x − θ), and invariant loss L(θ, d) = ρ(d − θ) with strictly convex ρ, Farrell (1964) established: (i) part (b) of Theorem 2, and (ii) the minimaxity of δU (X), and (iii) the admissibility of δU (X) for squared error loss ρ.

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