# Bias of An Estimator

Bias Of An Estimator

In statistics, the bias (or bias function) 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 ordinary English, the term bias is pejorative. In statistics, there are problems for which it may be good to use an estimator with a small, but nonzero, bias. In some cases, an estimator with a small bias may have lesser mean squared error or be median-unbiased (rather than mean-unbiased, the standard unbiasedness property). The property of median-unbiasedness is invariant under monotone transformations, while the property of mean-unbiasedness may be lost under nonlinear transformations.

### Other articles related to "bias of an estimator":

Bias Of An Estimator - Bayesian View
... Fundamentally, the difference between the Bayesian approach and the sampling-theory approach above is that in the sampling-theory approach the parameter is taken as fixed, and then probability distributions of a statistic are considered, based on the predicted sampling distribution of the data ... For a Bayesian, however, it is the data which is known, and fixed, and it is the unknown parameter for which an attempt is made to construct a probability distribution, using Bayes' theorem Here the second term, the likelihood of the data given the unknown parameter value θ, depends just on the data obtained and the modelling of the data generation process ...

### Famous quotes containing the word bias:

The solar system has no anxiety about its reputation, and the credit of truth and honesty is as safe; nor have I any fear that a skeptical bias can be given by leaning hard on the sides of fate, of practical power, or of trade, which the doctrine of Faith cannot down-weigh.
Ralph Waldo Emerson (1803–1882)