Cramer-rao lower bound example

1. How do you find the Cramer-Rao lower bound?
2. What is Cramer-Rao lower bound used for?
3. What are the regularity conditions for Cramer-Rao inequality?
4. What do you understand by minimum variance unbiased estimator?

How do you find 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 .

What is Cramer-Rao lower bound used for?

The Cramer-Rao lower bound (CRLB) expresses limits on the estimate variances for a set of deterministic parameters. We examine the CRLB as a useful metric to evaluate the performance of our SBP algorithm and to quickly compare the best possible resolution when investigating new detector designs.

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).

What do you understand by minimum variance unbiased estimator?

In statistics a minimum-variance unbiased estimator (MVUE) or uniformly minimum-variance unbiased estimator (UMVUE) is an unbiased estimator that has lower variance than any other unbiased estimator for all possible values of the parameter.