View source for Relative efficiency

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If, in a sampling study, we have the choice between different [[:category:sampling design|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 [[accuracy and precision|precision]] for a given effort. This involves the comparison with alternative estimators or/and other sampling designs:

If <math>\hat\theta_1</math> and <math>\hat\theta_2</math> are two unbiased estimators, relative efficiency is simply calculated as the ratio of the error variances of the two estimators. 

:<math>RE=\frac{V(\hat\theta_1)}{V(\hat\theta_2)}</math>

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]]