GCCV.S: The generalized correlated cross-validation (GCCV) score.

In fda.usc: Functional Data Analysis and Utilities for Statistical Computing

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

GCCV = \frac{\sum_{i=1}^n {(y_{i} - \hat{y}_{i, b})}^2}{(1 - \frac{tr(C)}{n})^2}

where C = 2S\Sigma(\theta) - S\Sigma(\theta)S'
and \Sigma is the n \times n covariance matrix with cor(\epsilon_i, \epsilon_j) = \sigma.

Here, S is the smoothing matrix, and there are options for C:

• A.- If C = 2S\Sigma - S\Sigma S

• B.- If C = S\Sigma

• C.- If C = S\Sigma S'

with \Sigma as the n \times n covariance matrix and cor(\epsilon_i, \epsilon_j) = \sigma.

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 [e-mail]

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., Munoz, P., and Dominguez, A. Predicting seasonal influenza transmission using Functional Regression Models with Temporal Dependence.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 April 4, 2025, 4:35 a.m.