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
xm
), wheren
is the number of curves andm
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 {
# }