Editing Estimator (section)

===Mean squared error===
The [[mean squared error]] of <math>\widehat{\theta}</math> is defined as the expected value (probability-weighted average, over all samples) of the squared errors; that is,
:<math>\operatorname{MSE}(\widehat{\theta}) = \operatorname{E}[(\widehat{\theta}(X) - \theta)^2].</math>
It is used to indicate how far, on average, the collection of estimates are from the single parameter being estimated. Consider the following analogy. Suppose the parameter is the [[Bullseye (target)|bull's-eye of a target]], the estimator is the process of shooting arrows at the target, and the individual arrows are estimates (samples). Then high MSE means the average distance of the arrows from the bull's eye is high, and low MSE means the average distance from the bull's eye is low. The arrows may or may not be clustered. For example, even if all arrows hit the same point, yet grossly miss the target, the MSE is still relatively large. However, if the MSE is relatively low then the arrows are likely more highly clustered (than highly dispersed) around the target.