Loss function: Difference between revisions

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Frequentist expected loss: convert to citeq
Selecting a loss function: convert to citeq
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==Selecting a loss function==
Sound statistical practice requires selecting an estimator consistent with the actual acceptable variation experienced in the context of a particular applied problem. Thus, in the applied use of loss functions, selecting which statistical method to use to model an applied problem depends on knowing the losses that will be experienced from being wrong under the problem's particular circumstances.<ref>{{cite book citeq|last=Pfanzagl |first=J. |year=1994 |title=Parametric Statistical Theory |___location=Berlin |publisher=Walter de Gruyter |isbn=978-3-11-013863-4 Q130238834}}</ref>
 
A common example involves estimating "[[___location parameter|___location]]". Under typical statistical assumptions, the [[mean]] or average is the statistic for estimating ___location that minimizes the expected loss experienced under the [[least squares|squared-error]] loss function, while the [[median]] is the estimator that minimizes expected loss experienced under the absolute-difference loss function. Still different estimators would be optimal under other, less common circumstances.