Mean squared prediction error

In <a href="/facts/Statistics/DNPsKGYU">statistics</a> the mean squared prediction error (MSPE), also known as mean squared error of the predictions, of a <a href="/facts/Smoothing/2svFjsbI">smoothing</a>, <a href="/facts/Curve_fitting/zrLKw6Xj">curve fitting</a>, or <a href="/facts/Regression_(statistics)/n6z5Tf7K">regression</a> procedure is the <a href="/facts/Expected_value/1XV0JKL8">expected value</a> of the <a href="/facts/Square_(algebra)/Jzpq0R0z">squared</a> prediction errors (PE), the <a href="/facts/Squared_deviation/qMoU6JGp">square difference</a> between the fitted values implied by the predictive function 
 
 
 
 
 
 
 g
 ^
 
 
 
 
 
 {\displaystyle {\widehat {g}}}
 
 and the values of the (unobservable) <a href="/facts/True_value/bhaUFWsB">true value</a> g. It is an inverse measure of the explanatory power of 
 
 
 
 
 
 
 g
 ^
 
 
 
 ,
 
 
 {\displaystyle {\widehat {g}},}
 
 and can be used in the process of <a href="/facts/Cross-validation_(statistics)/pDWg8s0e">cross-validation</a> of an estimated model.
Knowledge of g would be required in order to calculate the MSPE exactly; in practice, MSPE is estimated.

Mean squared prediction error open-in-new

Mean squared prediction error