fda.usc (version 2.1.0)

CV.S: The cross-validation (CV) score

Description

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

Usage

CV.S(y, S, W = NULL, trim = 0, draw = FALSE, metric = metric.lp, ...)

Value

Returns CV score calculated for input parameters.

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.

Author

Manuel Febrero-Bande, Manuel Oviedo de la Fuente

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.

See Also

See Also as optim.np
Alternative method: GCV.S

Examples

if (FALSE) {
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
}