Let t be a location invariant estimator of in a, Basic Statistics

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Let t be a location invariant estimator of in a

Let T be a location invariant estimator of µ in a one-parameter location problem. Show that T is an MRIE under the squared error loss if and only if T is unbiased and E[T (X)U(X)] = 0 for any U(X) satisfying U(x₁ + c, ..., x_n + c) = U(x) for any c, E[U(X)] = 0 for any µ, and Var(U) < ∞.="">

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