Editing Estimator (section)

===Consistency===
{{Main|Consistent estimator}}
A '''consistent estimator''' is an estimator whose sequence of estimates [[convergence in probability|converge in probability]] to the quantity being estimated as the index (usually the [[sample size]]) grows without bound. In other words, increasing the sample size increases the probability of the estimator being close to the population parameter.

Mathematically, an estimator is a consistent estimator for [[parameter]] ''θ'', if and only if for the sequence of estimates {{nowrap|{''t<sub>n</sub>''; ''n'' ≥ 0}}}, and for all {{nowrap|''ε'' > 0}}, no matter how small, we have
:<math>
\lim_{n\to\infty}\Pr\left\{
\left|
t_n-\theta\right|<\varepsilon
\right\}=1
</math>.

The consistency defined above may be called weak consistency. The sequence is ''strongly consistent'', if it [[Almost sure convergence|converges almost surely]] to the true value.

An estimator that converges to a ''multiple'' of a parameter can be made into a consistent estimator by multiplying the estimator by a [[scale factor]], namely the true value divided by the asymptotic value of the estimator. This occurs frequently in [[Scale parameter#Estimation|estimation of scale parameters]] by [[Statistical dispersion#Measures of statistical dispersion|measures of statistical dispersion]].