Cramér-Rao lower bound

1. Why is Cramer-Rao lower bound?
2. How do you calculate Cramer-Rao lower bound?
3. Can Cramer-Rao lower bound be negative?
4. What is the Cramer-Rao lower bound for the variance of unbiased estimator of the parameter?

Why is Cramer-Rao lower bound?

The Cramer-Rao Lower Bound (CRLB) gives a lower estimate for the variance of an unbiased estimator. Estimators that are close to the CLRB are more unbiased (i.e. more preferable to use) than estimators further away.

How do you calculate 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 .

Can Cramer-Rao lower bound be negative?

If the data points are on average below the true population mean, then the score is negative.

What is the Cramer-Rao lower bound for the variance of unbiased estimator of the parameter?

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.