GCV.S

The generalized correlated cross-validation (GCCV) score

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

Usage

GCV.S(
  y,
  S,
  criteria = "GCV",
  W = NULL,
  trim = 0,
  draw = FALSE,
  metric = metric.lp,
  ...
)

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.

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

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

Aliases

• 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 {
 
# }