Prediction error

Prediction error is the expected loss of a fitted rule on a new observation from the target distribution.

Test error is the average loss on an independent test set and estimates prediction error when the test set has not influenced model fitting or selection.

For a predictor $\hat{f}$ and an independent response $Y^{\ast }$ at covariate $X^{\ast }$, mean squared prediction error is $\mathbb{E}[(Y^{\ast }-\hat{f}(X^{\ast }){)}^2]$.