Theorem 5.2.2

Information Lower Bound in Multiparameter Case

Suppose T = T(X) is an estimator of g(θ) with bias b(θ) and finite variance, that is, EθT=g(θ)+b(θ)si227_e and VarθT<si228_ewhere the family f(x,θ),θΘRksi222_e satisfies regularity Conditions 1, 2, and 3. Then,

VarθTTg(θ)+b(θ)I(θ)1g(θ)+b(θ).

si230_e

Example 5.2.1

In a random sample X1,,Xn from N(μ,σ2), ...

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