Mean squared prediction error

In statistics the mean squared prediction error (MSPE), also known as mean squared error of the predictions, of a smoothing, curve fitting, or regression procedure is the expected value of the squared prediction errors (PE), the square difference between the fitted values implied by the predictive function ${\widehat {g}}$ and the values of the (unobservable) true value g. It is an inverse measure of the explanatory power of ${\widehat {g}},$ and can be used in the process of cross-validation of an estimated model. Knowledge of g would be required in order to calculate the MSPE exactly; in practice, MSPE is estimated.^[1]

^ Pindyck, Robert S.; Rubinfeld, Daniel L. (1991). "Forecasting with Time-Series Models". Econometric Models & Economic Forecasts (3rd ed.). New York: McGraw-Hill. pp. 516–535. ISBN 0-07-050098-3.

[1] Pindyck, Robert S.; Rubinfeld, Daniel L. (1991). "Forecasting with Time-Series Models". Econometric Models & Economic Forecasts (3rd ed.). New York: McGraw-Hill. pp. 516–535. ISBN 0-07-050098-3.

[1]