Let X1, . . . , Xn form a random sample from a distribution for which the p.d.f. or the p.f. is f (x|), where

Let X1, . . . , Xn form a random sample from a distribution for which the p.d.f. or the p.f. is f (x|θ), where θ ∈ Ω. Suppose that the value of θ must be estimated, and that T is a sufficient statistic for θ. Let δ be an arbitrary estimator of θ, and let δ0 be another estimator defined by the relation δ0 = E(δ|T ). Show that for every value of θ ∈ Ω,
Eθ (|δ0 − θ|) ≤ Eθ (|δ − θ|).