Definition:Estimator

Definition

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 $\theta$.

A particular realization of $\hat \theta$ is called an estimate of $\theta$.

Sources

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