is consistent, as it must converge to the correct value. Biased but consistent Alternatively, an estimator can be biased but consistent. For example, if the mean is estimated by it is biased, but as , 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 instead of the degrees of freedom ), 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 be a sequence of estimators for . We can see that , , and the bias does not converge to zero. See also Efficient estimator Fisher consistency — alternative, although rarely used concept of consistency for the estimators Regression dilution Statistical hypothesis testing Instrumental variables estimation Notes References . External links by Mark Thoma Estimator Asymptotic theory (statistics)