## 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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