optimum estimator - определение. Что такое optimum estimator
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Что (кто) такое optimum estimator - определение

EXPECTATION OF ERROR OF ESTIMATION
Unbiased estimator; Biased estimator; Estimator bias; Unbiased estimate; Unbiasedness

Estimator         
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USED IN MATHEMATICAL STATISTICS TO DETERMINE AN ESTIMATED VALUE
Efficiency bound; Restricted estimate; Unrestricted estimate; Asymptotically unbiased; Estimators; Asymptotically normal estimator; Parameter estimate; Universal estimator; Estimated value; Statistical estimate; Estimate (statistics)
·noun One who estimates or values; a valuer.
Estimator         
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USED IN MATHEMATICAL STATISTICS TO DETERMINE AN ESTIMATED VALUE
Efficiency bound; Restricted estimate; Unrestricted estimate; Asymptotically unbiased; Estimators; Asymptotically normal estimator; Parameter estimate; Universal estimator; Estimated value; Statistical estimate; Estimate (statistics)
In statistics, an estimator is a rule for calculating an estimate of a given quantity based on observed data: thus the rule (the estimator), the quantity of interest (the estimand) and its result (the estimate) are distinguished. For example, the sample mean is a commonly used estimator of the population mean.
Bias of an estimator         
In statistics, the bias of an estimator (or bias function) 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.

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Bias of an estimator

In statistics, the bias of an estimator (or bias function) 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. In statistics, "bias" is an objective property of an estimator. Bias is a distinct concept from consistency: consistent estimators converge in probability to the true value of the parameter, but may be biased or unbiased; see bias versus consistency for more.

All else being equal, an unbiased estimator is preferable to a biased estimator, although in practice, biased estimators (with generally small bias) are frequently used. When a biased estimator is used, bounds of the bias are calculated. A biased estimator may be used for various reasons: because an unbiased estimator does not exist without further assumptions about a population; because an estimator is difficult to compute (as in unbiased estimation of standard deviation); because a biased estimator may be unbiased with respect to different measures of central tendency; because a biased estimator gives a lower value of some loss function (particularly mean squared error) compared with unbiased estimators (notably in shrinkage estimators); or because in some cases being unbiased is too strong a condition, and the only unbiased estimators are not useful.

Bias can also be measured with respect to the median, rather than the mean (expected value), in which case one distinguishes median-unbiased from the usual mean-unbiasedness property. Mean-unbiasedness is not preserved under non-linear transformations, though median-unbiasedness is (see § Effect of transformations); for example, the sample variance is a biased estimator for the population variance. These are all illustrated below.