4.6 Relative Efficiency

SW 3.1

If \(\hat{\theta}_1\) and \(\hat{\theta}_2\) are two unbiased estimators of \(\theta\), then \(\hat{\theta}_1\) is more efficient than \(\hat{\theta}_2\) if \(\mathrm{var}(\hat{\theta}_1) < \mathrm{var}(\hat{\theta}_2)\).

Relative efficiency gives us a way to rank unbiased estimators.