The cross-validation (CV) score

Description

The cross-validation (CV) score.

Usage

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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 manuel.oviedo@usc.es

References

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

See Also

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

Examples

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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,3,Ker.unif)
 S7 <- S.KNN(tt,5,Ker.unif)
 cv6 <- CV.S(x, S6)
 cv7 <- CV.S(x, S7)
 cv6;cv7
 

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