Estimator Estimator From Wikipedia, the free encyclopedia. In statistics, an estimator is a function of the known data that is used to estimate an unknown parameter; an estimate is the result from the actual application of the function to a particular set of data. Many different estimators are possible for any given parameter. Some criterion is used to choose between the estimators, although it is often the case that a criterion cannot be used to clearly pick one estimator over another. There are two types of estimators: point estimators and interval estimators. Contents showTocToggle('show','hide') 1 Point estimators 2 Consistency 3 Efficiency 4 Other properties 5 See also Point estimators For a point estimator θ of parameter θ: The bias of θ is defined as B(θ) = E[θ] − θ θ is an unbiased estimator of θ iff B(θ) = 0 for all θ The mean square error of θ is defined as MSE(θ) = E[(θ − θ)2] MSE(θ) = V(θ) + (B(θ))2 where V(X) is the variance of X and E(X) is the expected value of X. The standard deviation of an estimator of θ (the square root of the variance), or an estimate of the standard deviation of an estimator of θ, is called the standard error of θ. Consistency A consistent estimator is an estimator that converges in probability to the quantity being estimated as the sample size grows. An estimator <math>t_n<math> (where n is the sample size) is a consistent estimator for parameter <math> heta<math> if and only if, for all <math>epsilon > 0<math>, no matter how small, we have <math> lim_{n oinfty}{ m Prob}left{ left| t_n- heta ight| Quelle "Estimator" : Wikipedia.org Main page for "Estimator"