Rule for calculating an estimate of a given quantity based on observed data
An estimate is not the same thing as an estimator: an estimate is a specific value dependent on only the dataset while an estimator is a method for estimation that is realized through random variables.
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.[1] For example, the sample mean is a commonly used estimator of the population mean.
There are point and interval estimators. The point estimators yield single-valued results. This is in contrast to an interval estimator, where the result would be a range of plausible values. "Single value" does not necessarily mean "single number", but includes vector valued or function valued estimators.
Estimation theory is concerned with the properties of estimators; that is, with defining properties that can be used to compare different estimators (different rules for creating estimates) for the same quantity, based on the same data. Such properties can be used to determine the best rules to use under given circumstances. However, in robust statistics, statistical theory goes on to consider the balance between having good properties, if tightly defined assumptions hold, and having worse properties that hold under wider conditions.
^Mosteller, F.; Tukey, J. W. (1987) [1968]. "Data Analysis, including Statistics". The Collected Works of John W. Tukey: Philosophy and Principles of Data Analysis 1965–1986. Vol. 4. CRC Press. pp. 601–720 [p. 633]. ISBN 0-534-05101-4 – via Google Books.
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estimator approaches the MAP estimator, provided that the distribution of θ {\displaystyle \theta } is quasi-concave. But generally a MAP estimator is...
{X}},} an estimator (estimation rule) δ M {\displaystyle \delta ^{M}\,\!} is called minimax if its maximal risk is minimal among all estimators of θ {\displaystyle...
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