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.