**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.

Read more about Bias Of An Estimator: Definition, Median-unbiased Estimators, Bias With Respect To Other Loss Functions, Effect of Transformations, Bias, Variance and Mean Squared Error, Bayesian View

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### 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)