Relative Efficiency
If and are estimators for the parameter, then is said to dominate if:
- its mean squared error (MSE) is smaller for at least some value of
- the MSE does not exceed that of for any value of θ.
Formally, dominates if
holds for all, with strict inequality holding somewhere.
The relative efficiency is defined as
Although is in general a function of, in many cases the dependence drops out; if this is so, being greater than one would indicate that is preferable, whatever the true value of .
Read more about this topic: Efficient Estimator
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