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GCV Score for Basis Representation

Source: R/basis.R
basis.gcv.Rd

Computes the Generalized Cross-Validation score for a basis representation. Lower GCV indicates better fit with appropriate complexity.

Usage

basis.gcv(
  fdataobj,
  nbasis,
  type = c("bspline", "fourier"),
  lambda = 0,
  pooled = TRUE
)

Arguments

fdataobj

An fdata object.

nbasis

Number of basis functions.

type

Basis type: "bspline" (default) or "fourier".

lambda

Smoothing/penalty parameter (default 0, no penalty).

pooled

Logical. If TRUE (default), compute a single GCV across all curves. If FALSE, compute GCV for each curve and return the mean.

Value

The GCV score (scalar).

Details

GCV is computed as: $$GCV = \frac{RSS/n}{(1 - edf/n)^2}$$ where RSS is the residual sum of squares and edf is the effective degrees of freedom (trace of the hat matrix).

When pooled = TRUE, the criterion is computed globally across all curves. When pooled = FALSE, the criterion is computed for each curve separately and the mean is returned. Use pooled = FALSE when curves have heterogeneous noise levels.

Examples

t <- seq(0, 1, length.out = 50)
X <- matrix(sin(2 * pi * t) + rnorm(50, sd = 0.1), nrow = 1)
fd <- fdata(X, argvals = t)

# Compare GCV for different nbasis
gcv_5 <- basis.gcv(fd, nbasis = 5)
gcv_10 <- basis.gcv(fd, nbasis = 10)
gcv_20 <- basis.gcv(fd, nbasis = 20)