Howtosignalprocessing
- What is Cramer-Rao lower bound and MSE?
- Why is the Cramer-Rao lower bound important?
- How is Cramer-Rao bound calculated?
- How do you derive the Cramer-Rao lower bound?
What is Cramer-Rao lower bound and MSE?
Derived in the 1940s, the Cramer-Rao bound gives us a lower bound for the variance/MSE of unbiased estimators. This means that the best possible estimator for a given parameter will have an MSE dictated by the bound. If we have equality in the bound, then we know that the estimator is efficient!
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.
How is Cramer-Rao bound calculated?
The function 1/I(θ) is often referred to as the Cramér-Rao bound (CRB) on the variance of an unbiased estimator of θ. I(θ) = −Ep(x;θ) ∂2 ∂θ2 logp(X;θ) . and, by Corollary 1, X is a minimum variance unbiased (MVU) estimator of λ.
How do you derive the Cramer-Rao lower bound?
Alternatively, we can compute the Cramer-Rao lower bound as follows: ∂2 ∂p2 log f(x;p) = ∂ ∂p ( ∂ ∂p log f(x;p)) = ∂ ∂p (x p − m − x 1 − p ) = −x p2 − (m − x) (1 − p)2 .
