Index: The Book of Statistical Proofs ▷ General Theorems ▷ Estimation theory ▷ Basic concepts of estimation ▷ Estimator

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”.

 
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Metadata: ID: D208 | shortcut: est | author: JoramSoch | date: 2024-11-01, 14:26.