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.

Read more about Bias Of An EstimatorDefinition, 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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Bias Of An Estimator - 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)