Introduction to turbulence/Statistical analysis/Generalization to the estimator of any quantity
From CFD-Wiki
Similar relations can be formed for the estimator of any function of the random variable say . For example, an estimator for the average of
based on
realizations is given by:
| (2) |
where . It is straightforward to show that this estimator is unbiased, and its variability (squared) is given by:
| (2) |
Example: Suppose it is desired to estimate the variability of an estimator for the variance based on a finite number of samples as:
| (2) |
(Note that this estimator is not really very useful since it presumes that the mean value, , is known, whereas in fact usually only
is obtainable).
Answer
Let in equation 2.55 so that
,
and
. Then: