# GCV.S

0th

Percentile

##### The generalized correlated cross-validation (GCCV) score

Compute the generalized correlated cross-validation (GCV) score.

Keywords
utilities
##### Usage
GCV.S(
y,
S,
criteria = "GCV",
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

criteria

The penalizing function. By default "Rice" criteria. Possible values are "GCCV1", "GCCV2", "GCCV3", "GCV".

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: $$GCCV=\frac{\sum_{i=1}^n {y_{i}-\hat{y}_{i,b}}^2}{1-\frac{tr(C)}{n}^2}$$ where $$S$$ is the smoothing matrix $$S$$ and: A.-If $$C=2S\Sigma - S\Sigma S$$ B.-If $$C=S\Sigma$$ C.-If $$C=S\Sigma S'$$ with $$\Sigma$$ is the n x n covariance matrix with $$cor(\epsilon_i,\epsilon_j ) =\sigma$$ Note: Provided that $$C = I$$ and the smoother matrix S is symmetric and idempotent, as is the case for many linear fitting techniques, the trace term reduces to $$n - tr[S]$$, which is proportional to the familiar denominator in GCV.

##### Value

Returns GCV score calculated for input parameters.

##### References

Wasserman, L. All of Nonparametric Statistics. Springer Texts in Statistics, 2006. Hardle, W. Applied Nonparametric Regression. Cambridge University Press, 1994. Febrero-Bande, M., Oviedo de la Fuente, M. (2012). Statistical Computing in Functional Data Analysis: The R Package fda.usc. Journal of Statistical Software, 51(4), 1-28. http://www.jstatsoft.org/v51/i04/

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

• GCV.S
##### Examples
# NOT RUN {
data(phoneme)
mlearn<-phoneme\$learn
tt<-1:ncol(mlearn)
S1 <- S.NW(tt,2.5)
S2 <- S.LLR(tt,2.5)
gcv1 <- GCV.S(mlearn, S1)
gcv2 <- GCV.S(mlearn, S2)
gcv3 <- GCV.S(mlearn, S1,criteria="AIC")
gcv4 <- GCV.S(mlearn, S2,criteria="AIC")
gcv1; gcv2; gcv3; gcv4
# }
# NOT RUN {

# }

Documentation reproduced from package fda.usc, version 2.0.1, License: GPL-2

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