Definition:Mean Squared Error of Estimator

Definition

Let $\theta$ be a population parameter of some population.

Let $\mathbf X$ be a random sample from this population.

Let $\hat \theta$ be an estimator of $\theta$.

The mean squared error of $\hat \theta$ is defined by:

$\map {\operatorname {MSE} } {\hat \theta} = \expect {\paren {\map {\hat \theta} {\mathbf X} - \theta}^2} $

Also known as

The term mean squared error is commonly abbreviated to m.s.e., M.S.E. or MSE.

Sources

• 2011: Morris H. DeGroot and Mark J. Schervish: Probability and Statistics (4th ed.): $4.5$: The Mean and the Median: Definition $4.5.2$