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) |