Let X1,...,Xn be iid Poisson(A), and let and S2 denote the sample mean and variance, respectively. We now complete Example 7.3.8 in a different way. There we used the Cramer-Rao Bound; now we use completeness. (a) Prove that is the best unbiased estimator of without using the Cramer-Rao Theorem. (b) Prove the rather remarkable identity E(S2|) =
Let X1,...,Xn be iid Poisson(A), and let and S2 denote the sample mean and variance, respectively. We now complete Example 7.3.8 in a different way. There we used the Cramer-Rao Bound; now we use completeness.
(a) Prove that is the best unbiased estimator of λ without using the Cramer-Rao Theorem.
(b) Prove the rather remarkable identity E(S2|) = , and use it to explicitly demonstrate that VarS2 > Var.
(c) Using completeness, can a general theorem be formulated for which the identity in part (b) is a special case?
(a) Prove that is the best unbiased estimator of λ without using the Cramer-Rao Theorem.
(b) Prove the rather remarkable identity E(S2|) = , and use it to explicitly demonstrate that VarS2 > Var.
(c) Using completeness, can a general theorem be formulated for which the identity in part (b) is a special case?
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a. Because the Poisson family is an exponential family with t(x) = x, i X i is a complet…View the full answer
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