An estimator is a rule that tells how to calculate an estimate based on the measurements contained in a sample. For example, the sample mean x^_ is an estimator for the population mean μ. The mean square error of an estimator θ^~ is defined by MSE congruent 〈(θ^~ - θ)^2 〉. Let B be the estimator bias, then MSE | = | 〈[(θ^~ - 〈θ^~ 〉) + B(θ^~)]^2 〉 | = | 〈(θ^~ - 〈θ^~ 〉)^2 〉 + B^2(θ^~) | congruent | V(θ^~) + B^2(θ^~), where V is the estimator variance.

error | estimate | estimator bias | expectation value | h-statistic | k-statistic | polyache | polykay | sample central moment | sample mean | sample variance | unbiased estimator