Definition: Mean squared error
Index:
The Book of Statistical Proofs ▷
General Theorems ▷
Estimation theory ▷
Point estimates ▷
Mean squared error
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Metadata: ID: D173 | shortcut: mse | author: JoramSoch | date: 2022-03-27, 23:41.
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 $\hat{\theta}$.
- Wikipedia (2022): "Estimator"; in: Wikipedia, the free encyclopedia, retrieved on 2022-03-27; URL: https://en.wikipedia.org/wiki/Estimator#Mean_squared_error.
Metadata: ID: D173 | shortcut: mse | author: JoramSoch | date: 2022-03-27, 23:41.