Mean squared prediction error: Difference between revisions

Revision as of 15:49, 24 October 2017

Revision as of 09:45, 16 May 2018

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{{Unreferenced|date=December 2009}}

{{expert-subject|statistics|reason=no source, and notation/definition problems regarding ''L''}}

In [[statistics]] the '''mean squared prediction error''' of a [[smoothing]] or [[curve fitting]] procedure is the expected value of the squared difference between the fitted values implied by the predictive function <math>\widehat{g}</math> and the values of the (unobservable) function ''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.

If the smoothing or fitting procedure has [[operator matrix]] (i.e., hat matrix) ''L'', which maps the observed values vector <math>y</math> to predicted values vector <math>\hat{y}</math> via <math>\hat{y}=Ly,</math> then