The cross-validation (CV) score

Compute the leave-one-out cross-validation score.

Usage

CV.S(y, S, 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: Smoothing matrix, see S.NW, S.LLR or $S.KNN$.
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.

Value

Returns CV score calculated for input parameters.

Details

A.-If trim=0:
$$CV(h)=\frac{1}{n} \sum_{i=1}^{n}{\Bigg(\frac{y_i-r_{i}(x_i)}{(1-S_{ii})}\Bigg)^{2}w(x_{i})}$$ $S_{ii}$ is the ith diagonal element of the smoothing matrix $S$.

B.-If trim>0:
$$CV(h)=\frac{1}{l} \sum_{i=1}^{l}{\Bigg(\frac{y_i-r_{i}(x_i)}{(1-S_{ii})}\Bigg)^{2}w(x_{i})}$$ $S_{ii}$ is the ith diagonal element of the smoothing matrix $S$ and l the index of (1-trim) curves with less error.

References

Wasserman, L. All of Nonparametric Statistics. Springer Texts in Statistics, 2006.

Author

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

Examples

if (FALSE) { # \dontrun{
data(tecator)
x<-tecator$absorp.fdata
np<-ncol(x)
tt<-1:np
S1 <- S.NW(tt,3,Ker.epa)
S2 <- S.LLR(tt,3,Ker.epa)
S3 <- S.NW(tt,5,Ker.epa)
S4 <- S.LLR(tt,5,Ker.epa)
cv1 <- CV.S(x, S1)
cv2 <- CV.S(x, S2)
cv3 <- CV.S(x, S3)
cv4 <- CV.S(x, S4)
cv5 <- CV.S(x, S4,trim=0.1,draw=TRUE)
cv1;cv2;cv3;cv4;cv5
S6 <- S.KNN(tt,1,Ker.unif,cv=TRUE)
S7 <- S.KNN(tt,5,Ker.unif,cv=TRUE)
cv6 <- CV.S(x, S6)
cv7 <- CV.S(x, S7)
cv6;cv7
} # }