information:filtering, stylistic:tone, structural:reformatting
Consistency

A consistent sequence of estimators is a sequence of estimators that 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, a sequence of estimators { t; n ≥ 0 } is a consistent estimator for parameter θ if and only if, for all ε > 0, no matter how small, we have

The consistency defined above may be called weak consistency. The sequence is strongly consistent, if it 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 estimation of scale parameters by measures of statistical dispersion.