added definition "est"

Author: JoramSoch

D/est.md

@@ -0,0 +1,36 @@
+---
+layout: definition
+mathjax: true
+
+author: "Joram Soch"
+affiliation: "BCCN Berlin"
+e_mail: "joram.soch@bccn-berlin.de"
+date: 2024-11-01 14:26:04
+
+title: "Estimand, estimator and estimate"
+chapter: "General Theorems"
+section: "Estimation theory"
+topic: "Basic concepts of estimation"
+definition: "Estimator"
+
+sources:
+  - authors: "Wikipedia"
+    year: 2024
+    title: "Estimator"
+    in: "Wikipedia, the free encyclopedia"
+    pages: "retrieved on 2024-11-01"
+    url: "https://en.wikipedia.org/wiki/Estimator#Definition"
+
+def_id: "D208"
+shortcut: "est"
+username: "JoramSoch"
+---
+
+
+**Definition:** Let $y \in \mathcal{Y}$ be [measured data](/D/data), governed by a [probability distribution](/D/dist) described by some [statistical parameter](/D/para) $\theta \in \Theta$. 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".