# GCV.S

##### The generalized correlated cross-validation (GCCV) score

Compute the generalized correlated cross-validation (GCV) score.

- Keywords
- utilities

##### Usage

```
GCV.S(
y,
S,
criteria = "GCV",
W = NULL,
trim = 0,
draw = FALSE,
metric = metric.lp,
...
)
```

##### Arguments

- y
Matrix of set cases with dimension (

`n`

x`m`

), where`n`

is the number of curves and`m`

are the points observed in each curve.- S
- criteria
The penalizing function. By default

*"Rice"*criteria. Possible values are*"GCCV1"*,*"GCCV2"*,*"GCCV3"*,*"GCV"*.- W
Matrix of weights.

- trim
The alpha of the trimming.

- draw
=TRUE, draw the curves, the sample median and trimmed mean.

- metric
Metric function, by default

`metric.lp`

.- …
Further arguments passed to or from other methods.

##### Details

A.-If `trim=0`

:
$$GCCV=\frac{\sum_{i=1}^n {y_{i}-\hat{y}_{i,b}}^2}{1-\frac{tr(C)}{n}^2}$$
where \(S\) is the smoothing matrix \(S\) and:
A.-If \(C=2S\Sigma - S\Sigma S\)
B.-If \(C=S\Sigma\)
C.-If \(C=S\Sigma S'\)
with \(\Sigma\) is the n x n covariance matrix with
\(cor(\epsilon_i,\epsilon_j ) =\sigma\)
Note: Provided that \(C = I\) and the smoother matrix S is symmetric and idempotent, as is the case for many linear fitting techniques, the trace term reduces to \(n - tr[S]\), which is proportional to the familiar denominator in GCV.

##### Value

Returns GCV score calculated for input parameters.

##### References

Wasserman, L. *All of Nonparametric Statistics*. Springer Texts in Statistics, 2006.
Hardle, W. *Applied Nonparametric Regression*. Cambridge University Press, 1994.
Febrero-Bande, M., Oviedo de la Fuente, M. (2012). *Statistical Computing in Functional Data Analysis: The R Package fda.usc.*
Journal of Statistical Software, 51(4), 1-28. http://www.jstatsoft.org/v51/i04/

##### See Also

##### Examples

```
# NOT RUN {
data(phoneme)
mlearn<-phoneme$learn
tt<-1:ncol(mlearn)
S1 <- S.NW(tt,2.5)
S2 <- S.LLR(tt,2.5)
gcv1 <- GCV.S(mlearn, S1)
gcv2 <- GCV.S(mlearn, S2)
gcv3 <- GCV.S(mlearn, S1,criteria="AIC")
gcv4 <- GCV.S(mlearn, S2,criteria="AIC")
gcv1; gcv2; gcv3; gcv4
# }
# NOT RUN {
# }
```

*Documentation reproduced from package fda.usc, version 2.0.1, License: GPL-2*