Consistent Estimator Another way to measure the closeness of an estimator to the parameter Θ is in terms of consistency. If Θn is an estimator of Θ based on a random sample of n observations, is consistent for θ if




Thus, consistency is a large-sample property, describing the limiting behavior of Θn as n tends to infinity. It is usually difficult to prove consistency using the above definition, although it can be done from other approaches. To illustrate, show that is a consistent estimator of μ (when) σ2

X and X =