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

In fda.usc: Functional Data Analysis and Utilities for Statistical Computing

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, ...)

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

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

Returns CV score calculated for input parameters.

Author(s)

Manuel Febrero-Bande, Manuel Oviedo de la Fuente [e-mail]

References

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

See Also

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

Examples

## Not run: 
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

## End(Not run)
 

fda.usc documentation built on Oct. 17, 2022, 9:06 a.m.