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m →See also More: Manually undid revision 817300899 by 117.206.113.20 (talk) |
Clarify that "Without Bessel's correction" == using n |
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Alternatively, an estimator can be biased but consistent. For example if the mean is estimated by <math>{1 \over n} \sum x_i + {1 \over n}</math> it is biased, but as <math>n \rightarrow \infty</math>, it approaches the correct value, and so it is consistent.
Important examples include the [[sample variance]] and [[sample standard deviation]]. Without [[Bessel's correction]] (that is, when using the sample size ''n'' instead of the [[Degrees of freedom (statistics)|degrees of freedom]] ''n'' − 1), these are both negatively biased but consistent estimators. With the correction, the corrected sample variance is unbiased, while the corrected sample standard deviation is still biased, but less so, and both are still consistent: the correction factor converges to 1 as sample size grows.
Here is another example. Let <math>T_n</math> be a sequence of estimators for <math>\theta</math>.
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