Editing Estimator (section)

{{short description|Rule for calculating an estimate of a given quantity based on observed data}}
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In [[statistics]], an '''estimator''' is a rule for calculating an [[estimate]] of a given [[quantity]] based on [[Sample (statistics)|observed data]]: thus the rule (the estimator), the quantity of interest (the [[estimand]]) and its result (the estimate) are distinguished.<ref>{{cite book |last1=Mosteller |first1=F. |last2=Tukey |first2=J. W. |orig-year=1968 |chapter=Data Analysis, including Statistics |title=The Collected Works of John W. Tukey: Philosophy and Principles of Data Analysis 1965–1986 |volume=4 |publisher=CRC Press |year=1987 |isbn=0-534-05101-4 |pages=601–720 [p. 633] |chapter-url=https://books.google.com/books?id=C1guHWTlVVoC&pg=PA633 |via=[[Google Books]] }}</ref> For example, the [[sample mean]] is a commonly used estimator of the [[population mean]].

There are [[point estimator|point]] and [[interval estimator]]s. The [[point estimator]]s 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.