# GCCV.S: The generalized correlated cross-validation (GCCV) score. In fda.usc: Functional Data Analysis and Utilities for Statistical Computing

 GCCV.S R Documentation

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

### Description

The generalized correlated cross-validation (GCV) score.

### Usage

```GCCV.S(
y,
S,
criteria = "GCCV1",
W = NULL,
trim = 0,
draw = FALSE,
metric = metric.lp,
...
)
```

### Arguments

 `y` Response vectorith length `n` or 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` Smoothing matrix, see `S.NW`, `S.LLR` or S.KNN. `criteria` The penalizing function. By default "Rice" criteria. "GCCV1","GCCV2","GCCV3","GCV") 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

∑(y-y.fit)^2 / (1-tr(C)/n)^2

∑(y-y.fit)^2 / (1-tr(C)/n)^2

cor(ε_i,ε_j ) =σ

where S is the smoothing matrix S and:
A.-If C=2SΣ - SΣ S
B.-If C=SΣ
C.-If C=SΣ S'
with Σ is the n x n covariance matrix with cor(ε_i,ε_j ) =σ

### Value

Returns GCCV score calculated for input parameters.

### 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.

### Author(s)

Manuel Febrero-Bande, Manuel Oviedo de la Fuente manuel.oviedo@udc.es

### References

Carmack, P. S., Spence, J. S., and Schucany, W. R. (2012). Generalised correlated cross-validation. Journal of Nonparametric Statistics, 24(2):269–282.

Oviedo de la Fuente, M., Febrero-Bande, M., Pilar Munoz, and Dominguez, A. Predicting seasonal influenza transmission using Functional Regression Models with Temporal Dependence. arXiv:1610.08718. https://arxiv.org/abs/1610.08718

### See Also

See Also as `optim.np`.
Alternative method (independent case): `GCV.S`

### Examples

```## Not run:
data(tecator)
x=tecator\$absorp.fdata
x.d2<-fdata.deriv(x,nderiv=)
tt<-x[["argvals"]]
dataf=as.data.frame(tecator\$y)
y=tecator\$y\$Fat
# plot the response
plot(ts(tecator\$y\$Fat))

nbasis.x=11;nbasis.b=7
basis1=create.bspline.basis(rangeval=range(tt),nbasis=nbasis.x)
basis2=create.bspline.basis(rangeval=range(tt),nbasis=nbasis.b)
basis.x=list("x.d2"=basis1)
basis.b=list("x.d2"=basis2)
ldata=list("df"=dataf,"x.d2"=x.d2)
# No correlation
res.gls=fregre.gls(Fat~x.d2,data=ldata,
basis.x=basis.x,basis.b=basis.b)
# AR1 correlation
res.gls=fregre.gls(Fat~x.d2,data=ldata, correlation=corAR1(),
basis.x=basis.x,basis.b=basis.b)
GCCV.S(y,res.gls\$H,"GCCV1",W=res.gls\$W)
res.gls\$gcv

## End(Not run)
```

fda.usc documentation built on Oct. 17, 2022, 9:06 a.m.