Definition: Estimand, estimator and estimate
Index:
The Book of Statistical Proofs ▷
General Theorems ▷
Estimation theory ▷
Basic concepts of estimation ▷
Estimator
Sources:
Metadata: ID: D208  shortcut: est  author: JoramSoch  date: 20241101, 14:26.
Definition: Let $y \in \mathcal{Y}$ be measured data, governed by a probability distribution described by some statistical parameter $\theta \in \Theta$. Then, a function $\hat{\theta}: \mathcal{Y} \rightarrow \Theta$ exemplifying a rule for calculating an estimate of $\theta$ from $y$ is called an “estimator”. Estimation theory distinguishes:

the quantify of interest $\theta$ is called the “estimand”;

the rule $\hat{\theta}$ for estimating it is called “estimator”;

the result of estimation $\hat{\theta}(y)$ is called “estimate”.
 Wikipedia (2024): "Estimator"; in: Wikipedia, the free encyclopedia, retrieved on 20241101; URL: https://en.wikipedia.org/wiki/Estimator#Definition.
Metadata: ID: D208  shortcut: est  author: JoramSoch  date: 20241101, 14:26.