Index: The Book of Statistical ProofsGeneral Theorems ▷ Estimation theory ▷ Point estimates ▷ Mean squared error

Definition: Let $\hat{\theta}$ be an estimator of an unknown parameter $\hat{\theta}$ based on measured data $y$. Then, the mean squared error is defined as the expected value of the squared difference between the estimated value and the true value of the parameter:

\[\label{eq:mse} \mathrm{MSE} = \mathrm{E}_{\hat{\theta}}\left[ \left( \hat{\theta} - \theta \right)^2 \right] \; .\]

where $\mathrm{E}_{\hat{\theta}}\left[ \cdot \right]$ is expectation calculated over all possible samples $y$ leading to values of $\hat{\theta}$.


Metadata: ID: D173 | shortcut: mse | author: JoramSoch | date: 2022-03-27, 23:41.