Mean squared prediction error

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 ${\displaystyle {\widehat {g}}}$ and the values of the (unobservable) function g. It is an inverse measure of the explanatory power of ${\displaystyle {\widehat {g}},}$ and can be used in the process of 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 ${\displaystyle y}$ to predicted values vector ${\displaystyle {\hat {y}}}$ via ${\displaystyle {\hat {y}}=Ly,}$ then

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