thm. Cramer-Rao lower bound. Given estimator ,
If estimator is unbiased:
⇒ CRLB is a statement about the bound on the best possible precision [=efficiency] we can get.
→ If an estimator reaches the CRLB, it is deemed most efficient.
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thm. Cramer-Rao lower bound. Given estimator θ^,
If: E[θ^]=g(θ)⇒Var(θ^)≥I(θ)g′(θ)If estimator θ^ is unbiased:
Var(θ^)≥I(θ)1⇒ CRLB is a statement about the bound on the best possible precision [=efficiency] we can get.
→ If an estimator reaches the CRLB, it is deemed most efficient.