\begin{definition}[Definition:Mean Squared Error of Estimator]
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} $
\end{definition}