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Estimator

An estimator is a rule that tells how to calculate an estimate based on the measurements contained in a sample. For example, the sample mean x^_ is an estimator for the population mean mu.

The mean square error of an estimator theta^~ is defined by

MSE=<(theta^~-theta)^2>.
(1)

Let B be the estimator bias, then

MSE=<[(theta^~-<theta^~>)+B(theta^~)]^2>
(2)
=<(theta^~-<theta^~>)^2>+B^2(theta^~)
(3)
=V(theta^~)+B^2(theta^~),
(4)

where V is the estimator variance.

See also

Error, Estimate, Estimator Bias, Expectation Value, h-Statistic, k-Statistic, Polyache, Polykay, Sample Central Moment, Sample Mean, Sample Variance, Unbiased Estimator

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Cite this as:

Weisstein, Eric W. "Estimator." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/Estimator.html

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