fda.usc (version 1.1.0)

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

Description

The cross-validation (CV) 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

• res
  Returns CV score calculated for input parameters.

Details

Compute the leave-one-out cross-validation score. 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 min.np Alternative method: GCV.S

Examples

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.KNN(tt,3,Ker.epa)
 S4 <- S.NW(tt,5,Ker.epa)
 S5 <- S.LLR(tt,5,Ker.epa)
 S6 <- S.KNN(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, S5)
 cv6 <- CV.S(x, S6)
 cv7 <- CV.S(x, S4,trim=0.1,draw=TRUE)
 cv1;cv2;cv3;cv4;cv5;cv6;cv7