Mean squared prediction error: Difference between revisions

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{{Short description|Statistics concept}}

{{Multiple issues|

{{Unreferenced|date=December 2009}}

{{Expert needed|statistics|reason=no source, and notation/definition problems regarding ''L''|date=October 2019}}

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In [[statistics]] the '''mean squared prediction error''' ('''MSPE'''), also known as '''mean squared error of the predictions''', of a [[smoothing]], [[curve fitting]], or [[regression (statistics)|regression]] procedure is the [[expected value]] of the [[Square (algebra)|squared]] '''prediction errors''' ('''PE'''), the [[squared deviation|square difference]] between the fitted values implied by the predictive function <math>\widehat{g}</math> and the values of the (unobservable) [[true value]] ''g''. It is an inverse measure of the '''''explanatory power''''' of <math>\widehat{g},</math> and can be used in the process of [[cross-validation (statistics)|cross-validation]] of an estimated model.

*Knowledge of ''g'' would be required in order to calculate the MSPE exactly; in practice, MSPE is estimated.<ref>{{cite book |first1=Robert S. |last1=Pindyck |authorlink=Robert Pindyck |first2=Daniel L. |last2=Rubinfeld |authorlink2=Daniel L. Rubinfeld |title=Econometric Models & Economic Forecasts |___location=New York |publisher=McGraw-Hill |edition=3rd |year=1991 |isbn=0-07-050098-3 |chapter=Forecasting with Time-Series Models |pages=[https://archive.org/details/econometricmodel00pind/page/516 516–535] |chapter-url=https://archive.org/details/econometricmodel00pind/page/516 }}</ref>

Knowledge of ''g'' would be required in order to calculate the MSPE exactly; in practice, MSPE is estimated.

==Formulation==

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==See also==

* [[Akaike information criterion]]

* [[Bias-variance tradeoff]]

* [[Mean squared error]]

* [[Errors and residuals in statistics]]

* [[Law of total variance]]

* [[Mallows's Cp|Mallows's ''C_p'']]

{{Machine learning evaluation metrics}}

* [[Model selection]]

== Further readingReferences ==

{{reflist}}

*{{cite book |first1=Robert S. |last1=Pindyck |authorlink=Robert Pindyck |first2=Daniel L. |last2=Rubinfeld |authorlink2=Daniel L. Rubinfeld |title=Econometric Models & Economic Forecasts |___location=New York |publisher=McGraw-Hill |edition=3rd |year=1991 |isbn=0-07-050098-3 |chapter=Forecasting with Time-Series Models |pages=[https://archive.org/details/econometricmodel00pind/page/516 516–535] |chapter-url=https://archive.org/details/econometricmodel00pind/page/516 }}

{{Machine learning evaluation metrics}}

{{DEFAULTSORT:Mean Squared Prediction Error}}