Relative efficiency
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Revision as of 09:54, 28 October 2013
If, in a sampling study, we have the choice between different sampling designs or within the same sampling design between different estimators, we wish to apply the most efficient one; that is the one that yields best precision for a given effort. This involves the comparison with alternative estimators or/and other sampling designs:
If \(\hat\theta_1\) and \(\hat\theta_2\) are two unbiased estimators, relative efficiency is simply calculated as the ratio of the error variances of the two estimators.
\[RE=\frac{V(\hat\theta_1)}{V(\hat\theta_2)}\]
It should be observed that this is valid for \(var(\hat\theta)\) and not necessarily for \(\hat {var}(\hat\theta)\); that is, from data of a sampling study we can only estimate the relative efficiency.
