Relative efficiency
(Created page with "{{Ficontent}} If, in a sampling study, we have the choice between different sampling designs or within the same sampling design between different...") |
|||
| Line 8: | Line 8: | ||
It should be observed that this is valid for <math>var(\hat\theta)</math> and not necessarily for <math>\hat {var}(\hat\theta)</math>; that is, from data of a sampling study we can only estimate the relative efficiency. | It should be observed that this is valid for <math>var(\hat\theta)</math> and not necessarily for <math>\hat {var}(\hat\theta)</math>; that is, from data of a sampling study we can only estimate the relative efficiency. | ||
| − | [[Category:Introduction to sampling | + | [[Category:Introduction to sampling]] |
Latest revision as of 11:00, 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.
