# CV.S: The cross-validation (CV) score In fda.usc: Functional Data Analysis and Utilities for Statistical Computing

## Description

The cross-validation (CV) score.

## Usage

 `1` ```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.

## Details

Compute the leave-one-out cross-validation score.
A.-If `trim=0`:

CV(h)=1/n\, ∑_i ((y_i\, -\, r_{i}(x_i))\, /\, (1\, -\, S_ii))^2\, w(x_i),\, i=1,...,n

Sii is the ith diagonal element of the smoothing matrix S.

B.-If `trim>0`:

CV(h)=1/n\ ∑_i ((y_i-r_{i}(x_i))/(1-S_ii))^2 w(x_i),\, i=1,...,l

Sii is the ith diagonal element of the smoothing matrix S and l the index of `(1-trim)` curves with less error.

## Value

 `res` Returns CV score calculated for input parameters.

## Author(s)

Manuel Febrero-Bande, Manuel Oviedo de la Fuente [email protected]

## References

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

See Also as `min.np`
Alternative method: `GCV.S`
 ``` 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20``` ```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 ```