Crame'r-Rao lower bound

Definition

Let $h(\theta )$ be a function of parameter $\theta$. It can be simply $h(\theta )=\theta$. Now assume that $\hat{\theta }$ is a estimator of $\theta$. Then,

$$V(\hat{\theta })\ge \frac{\frac{dh(\theta )}{d\theta }}{nI(\theta )}$$

Observe that if $h(\theta )=\theta$ then derivative in the numerator is $0$ and

$$V(\hat{\theta })\ge \frac{1}{nI(\theta )}$$

where $I(\theta )$ is Fisher information.

TODO: Add conditions for CRLB