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
![\mathrm{E}
\left[ (T_1 - \theta)^2
\right]
\leq
\mathrm{E}
\left[ (T_2-\theta)^2
\right]](http://upload.wikimedia.org/math/3/7/2/372ed8d78dce9eef004a1e6e0c9de3dc.png)
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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