2.12 In an invariant estimation problem, write X = (T,W) where T is sufficient for , and W is ancillary. If the group of transformations

2.12 In an invariant estimation problem, write X = (T,W) where T is sufficient for θ, and W is ancillary. If the group of transformations is transitive, show:

(a) The best equivariant estimator δ∗ is the solution to mind Eθ [L(θ,d(x))|W = w].

(b) If e is the identity element of the group (g−1g = e), then δ∗ = δ∗(t,w) can be found by solving, for each w, mind Ee{L[e, d(T,w)]|W = w}.