Howtosignalprocessing
- Why is the Cramer-Rao lower bound important?
- What is the use of Cramer-Rao inequality?
- What are the regularity conditions for Cramer-Rao inequality?
- Does MLE always achieve Cramer-Rao lower bound?
Why is the Cramer-Rao lower bound important?
One of the most important applications of the Cramer-Rao lower bound is that it provides the asymptotic optimality property of maximum likelihood estimators. The Cramer-Rao theorem involves the score function and its properties which will be derived first.
What is the use of Cramer-Rao inequality?
The Cramér–Rao inequality is important because it states what the best attainable variance is for unbiased estimators. Estimators that actually attain this lower bound are called efficient. It can be shown that maximum likelihood estimators asymptotically reach this lower bound, hence are asymptotically efficient.
What are the regularity conditions for Cramer-Rao inequality?
If W(X) is unbiased for τ(θ), then W(X) attains the Cramer-Rao lower bound if and only if ∂ ∂θ logL(θ|x) = Sn(x|θ) = a(θ)[W(X) − τ(θ)] for some function a(θ).
Does MLE always achieve Cramer-Rao lower bound?
The mle does not always satisfy the condition so the CRLB might not be attainable..
