## Smoother Generalized Cross Validation

With the degrees of freedom of an estimate ,the mean squared error is given as

Cross-validation (CV) estimates the response at each *x*_{i} from the smoother that uses only the remaining *n*-1 observations. The resulting cross validation mean squared error is

where

is the fitted value at

*x*_{i} computed without the

*i*th observation.

The cross validation mean squared error can also be written as

where

is the

*i*th diagonal element of the

matrix (Hastie and Tibshirani 1990).

Generalized cross validation replaces by its average value, .The generalized cross validation mean squared error is

Note |
The function may have multiple minima, so the value estimated by SAS/INSIGHT software may be only a local minimum, not the global minimum. |

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