estimator A statistic used to estimate the value of a population parameter. An estimator X of a parameter θ is consistent if the probability of the difference between the two exceeding an arbitrarily small fixed number tends to zero as the sample size increases indefinitely. An estimator X is an unbiased estimator of the parameter θ if E(X) = θ, and it is a biased estimator otherwise (see expected value). The best unbiased estimator is the unbiased estimator with the minimum variance. The relative efficiency of two unbiased estimators X and Y is the ratio Var(Y)/Var(X) of their variances.
Estimators may be found in different ways, including the method of maximum likelihood (see likelihood) and the method of moments (see moment). |