Index: The Book of Statistical Proofs ▷ General Theorems ▷ Estimation theory ▷ Interval estimates ▷ Confidence interval

Definition: Let $y$ be a random sample from a probability distributions governed by a parameter of interest $\theta$ and quantities not of interest $\varphi$. A confidence interval for $\theta$ is defined as an interval $[u(y), v(y)]$ determined by the random variables $u(y)$ and $v(y)$ with the property

\[\label{eq:ci} \mathrm{Pr}(u(y) < \theta < v(y) \, \vert \, \theta, \varphi) = \gamma \quad \text{for all} \quad (\theta, \varphi) \; .\]

where $\gamma = 1 - \alpha$ is called the confidence level.

 
Sources:

Metadata: ID: D174 | shortcut: ci | author: JoramSoch | date: 2022-03-27, 23:56.