Editing Estimator (section)

===Asymptotic normality===
{{Main|Asymptotic normality}}
An [[asymptotic distribution#Asymptotic normality|asymptotically normal]] estimator is a consistent estimator whose distribution around the true parameter ''θ'' approaches a [[normal distribution]] with standard deviation shrinking in proportion to <math>1/\sqrt{n}</math> as the sample size ''n'' grows.  Using <math>\xrightarrow{D}</math> to denote [[Convergence of random variables#Convergence in distribution|convergence in distribution]], ''t<sub>n</sub>'' is [[Asymptotic normality|asymptotically normal]] if
:<math>\sqrt{n}(t_n - \theta) \xrightarrow{D} N(0,V),</math>
for some ''V''.

In this formulation ''V/n'' can be called the ''asymptotic variance'' of the estimator. However, some authors also call ''V'' the ''asymptotic variance''.
Note that convergence will not necessarily have occurred for any finite "n", therefore this value is only an approximation to the true variance of the estimator, while in the limit the asymptotic variance (V/n) is simply zero. To be more specific, the distribution of the estimator ''t<sub>n</sub>'' converges weakly to a [[dirac delta function]] centered at <math>\theta</math>.

The [[central limit theorem]] implies asymptotic normality of the [[sample mean]] <math>\bar X</math> as an estimator of the true mean.
More generally, [[maximum likelihood]] estimators are asymptotically normal under fairly weak regularity conditions — see the [[maximum likelihood#Asymptotics|asymptotics section]] of the maximum likelihood article. However, not all estimators are asymptotically normal; the simplest examples are found when the true value of a parameter lies on the boundary of the allowable parameter region.