Efficient Estimator

An Minimum Variance Unbiased Estimator is said to be efficient if and only if the following holds

$$\frac{\partial }{\partial \theta }\log p(x;\theta )=I(\theta )(g(x)-\theta )$$

For two functions $g(\cdot )$ and $I(\cdot )$. The MVU estimator is then $\hat{\theta }=g(x)$ and the corresponding variance of the estimator is $var(\hat{\theta })=I^{-1}(\theta )$.

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