**Consistent estimator - Wikipedia**
https://en.wikipedia.org/wiki/Consistent_estimator

OverviewBias versus consistencyDefinitionExamplesEstablishing consistencySee alsoNotesExternal linksAn estimator can be unbiased but not consistent. For example, for an iid sample {x 1,..., x n} one can use T n(X) = x n as the estimator of the mean E[X]. Note that here the sampling distribution of T n is the same as the underlying distribution (for any n, as it ignores all points but the last), so E[T n(X)] = E[X] and it is unbiased, but it does not converge to any value. However, if a sequence of estimators is unbiased and converges to a value, then it is consistent…

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