The generalized correlated cross-validation (GCCV) score
Compute the generalized correlated cross-validation (GCV) score.
GCV.S( y, S, criteria = "GCV", W = NULL, trim = 0, draw = FALSE, metric = metric.lp, ... )
y |
Matrix of set cases with dimension ( |
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 |
... |
Further arguments passed to or from other methods. |
A.-If trim=0:
∑(y-y.fit)^2 / (1-tr(C)/n)^2
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
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.
Returns GCV score calculated for input parameters.
Manuel Febrero-Bande, Manuel Oviedo de la Fuente manuel.oviedo@usc.es
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/
## 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 ## End(Not run)
Please choose more modern alternatives, such as Google Chrome or Mozilla Firefox.