Definition:Minimum Variance Unbiased Estimator
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Definition
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.
Hence, the smaller the variance, the greater its information content.
Also see
- Results about minimum variance unbiased estimators can be found here.
Sources
- 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): information: 2.
- 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): information: 2.