Definition:Mean Squared Error of Estimator

Definition
Let $\theta$ be a population parameter.

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

Let $\hat \theta \left({\mathbf X}\right)$ be an estimator of $\theta$ given $\mathbf X$.

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


 * $\operatorname{MSE} \left({\hat \theta}\right) = \mathbb E \left[{\left({\hat \theta \left({\mathbf X}\right) - \theta}\right)^2}\right]$