Estimator
Definition taught in Estimation, part of Statistical inference
Estimator
| Type | Definition |
| Taught in | Estimation |
| Part | Statistical inference |
| Worked examples | 1 |
An estimator of \theta is a statistic T=T(X_1,\ldots,X_n) whose value is used as a guess at \theta. Its observed value t=T(x_1,\ldots,x_n) is the estimate.
Examples
Ten thermometers
Worked example from Estimation
Ten thermometers are drawn at random from a large stock and tested. The results are 0,1,1,0,1,0,0,1,0,0, where 1 means the thermometer meets the standard.
Question. Write down a model and an estimate of the proportion p of compliant thermometers in the stock.
Solution. Let X_i=1 if the ith thermometer works. Drawing at random from a large stock makes the X_i close to independent, with \mathbb{P}(X_i=1)=p. The natural estimator is the sample proportion
\widehat p=\frac1{10}\sum_{i=1}^{10}X_i,
and its observed value is 4/10=0.4. The estimator is the recipe that would be applied to tomorrow’s ten thermometers. The estimate is the number 0.4 from today’s.
Used in
- Taught in Estimation, where the derivation and examples are.
- All 5 questions on Estimation
See also
Method of moments · Sample correlation coefficient · Likelihood function · Maximum likelihood · Invariance of maximum likelihood · Unbiased estimator · Mean squared error · Consistent estimator