One advantage of using a minimal sufficient statistic is that unbiased estimators will have smaller variance, as the following exercise will show. Suppose that T1 is sufficient and T2 is minimal sufficient, U is an unbiased estimator of θ, and define U1 = E(U|T1) and U2 = E(U1|T2).(a) Show that U2 = E(U1|T2). (b) Now use the conditional variance formula to show that Var U2 ≤ Var U1.

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