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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 and the values of the (unobservable) function g. It is an inverse measure of the explanatory power of 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 to predicted values vector via then
The MSPE can be decomposed into two terms (just like mean squared error is decomposed into bias and variance); however for MSPE one term is the sum of squared biases of the fitted values and another the sum of variances of the fitted values:
Note that knowledge of g is required in order to calculate MSPE exactly.