an estimator is a rule for calculating an estimate of a given quantity based on observed data.
for a given sample , the error of the estimator defined as , where is the parameter being estimated. the error, , depends not only on the estimator (the estimation formula or procedure), but also on the sample.
the mean squared error of is defined as the expected value (probability-weighted average, over all samples) of the squared errors; that is, .
it is used to indicate how far, on average, the collection of estimates are from the single parameter being estimated.