Estimator

Definition

An estimator $\hat{\theta }$ is a statistic $T(X_1,\dots X_n)$ which can be used for estimating the unknown parameter $\theta$. It is also said to be a function of a sample values.

For example

$$\sum \frac{x_i}{n}\text{ can be used to estimate }\mu$$

An estimator cannot contain the unknown parameter $\theta$.

Classical estimators

See

• Method of moments
• Maximum likelihood estimation
• Least squares estimation

Performance of the estimators

See Evaluating estimators.