GCV.S {fda.usc}

The generalized correlated cross-validation (GCCV) score

Description

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

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.

Author(s)

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

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. https://www.jstatsoft.org/v51/i04/

See Also

See Also as optim.np
Alternative method: CV.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

## End(Not run)