## Admissibility in location parameter problems |

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admissibility w.r.t. assume assumption 4(i assumptions of section basic idea Bayes estimators best invariant estimator Brown Chapter Chebyshev argument conclude inadmissibility Consider the transformed d9dx denote density f differential equation dimensional loss dominant Dominated Convergence Theorem easy to check equivalent to admissibility error terms estimator is admissible expand f x-9 F Farrell Finally finite priors gives gR(x higher order derivatives Jensen's inequality KF(x large 9 Lawrence Brown Lebesgue measure location parameter problems loss function Math matrix n-lxn nonsingular nonzero Note obvious paper prior density problem is equivalent prove admissibility quadratic loss question of admissibility random variable recall reduced problem region remainder term RQ s.t. s.t. for d(x sA(e satisfied Section 4.2 sequence of finite smooth Stat strictly convex Taylor expansion Taylors series Theorem transformed problem VF(x VR(x Wp(x WR(x YF(x Yp(x YR(x