Bias of an estimator
In statistics, the
bias of an estimator is the difference between this estimator's expected value and the true value of the parameter being estimated. An estimator or decision rule with zero bias is called
unbiased. Otherwise the estimator is said to be
biased. In statistics, "bias" is an objective statement about a function, and while not a desired property, it is not pejorative, unlike the ordinary English use of the term "bias". Bias can also be measured with respect to the median, rather than the mean, in which case one distinguishes
median-unbiased from the usual
mean-unbiasedness property. Bias is related to consistency in that consistent estimators are convergent and
asymptotically unbiased, though individual estimators in a consistent sequence may be biased; see bias versus consistency. All else equal, an unbiased estimator is preferable to a biased estimator, but in practice all else is not equal, and biased estimators are frequently used, generally with small bias. When a biased estimator is used, the bias is also estimated.