Category:Definitions/Minimum Variance Unbiased Estimators

This category contains definitions related to Minimum Variance Unbiased Estimators.
Related results can be found in Category:Minimum Variance Unbiased Estimators.

Let $S$ be a sample of $n$ observations from a probability distribution with frequency function $\map f {x, \theta}$.

Let it be assumed that certain regularity conditions apply.

Let it also be assumed that the extremes do not depend on $\theta$.

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Let $T$ be an unbiased estimator such that:

$\var T = \dfrac 1 I$

where:

$I = -n \map E {\dfrac {\partial^2 \ln f} {\partial \theta^2} }$

Then $\var T$ is called a minimum variance unbiased estimator.