Precision of estimators

An obvious question to ask about the estimators described in the previous sections is "How precise are they?" The precision of an estimator can be assessed in two ways: by resampling from a large dataset or by a single-sample prediction formula. The latter approach is the cheapest, and hence the most attractive whenever available. In the following section, the latter approach is taken to describe the precision of the Cavalieri method for estimating volume by point counting on systematic sections.

Suppose an unbiased estimator of some quantity \(Q\) is \(\hat{Q}\). A measure of the precision of \(\hat{Q}\), which depends on sampling design and sample size, is given by its coefficient of error (CE), which is defined as

$$ \mathrm{CE}(\hat{Q}) = \frac{+ \sqrt{\mathrm{Var}(\hat{Q})}}{Q}. $$

The positive square root of variance is also known as the standard error (SE).