Consider a location family pmicro micro isin rk on rk where, Ask an Expert

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Consider a location family {P_µ: µ ∈ R^k} on R^k, where P_µ = P₍_µ,Ik) is given in (2.10). Let l₀ ∈ R^k be a fixed vector and L(P, a) = L(kµ - ak), where a ∈ A = R^k and L(·) is a nonnegative Borel function on [0, ∞). Show that the family is invariant and the decision problem is invariant under the transformation g(X) = X +cl₀, c ∈ R. Find an invariant decision rule.

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