Definition:Estimator

Definition

An estimator is a statistic used to establish an approximate value of a population parameter.

Let $X_1, X_2, \ldots, X_n$ be random variables.

Let the joint distribution of $X_1, X_2, \ldots, X_n$ be indexed by a population parameter $\theta$.

Let $\delta: \R^n \to \R$ be a real-valued function.

The random variable $\hat \theta = \map \delta {X_1, X_2, \ldots, X_n}$ is called an estimator of $\theta$.

Estimate

An estimate is a particular realization of an estimator.

Also see

• Results about estimators can be found here.

Sources

• 1989: Ephraim J. Borowski and Jonathan M. Borwein: Dictionary of Mathematics ... (previous) ... (next): estimator
• 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): estimator
• 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): estimator
• 2011: Morris H. DeGroot and Mark J. Schervish: Probability and Statistics (4th ed.): $7.4$: Bayes Estimators: Definition $7.4.1$