Cross-Validation for Basis Function Number Selection — fdata2basis_cv • fdars

Selects the optimal number of basis functions using k-fold cross-validation or generalized cross-validation.

Usage

fdata2basis_cv(
  fdataobj,
  nbasis.range = 4:20,
  type = c("bspline", "fourier"),
  criterion = c("GCV", "CV", "AIC", "BIC"),
  kfold = 10,
  lambda = 0
)

Arguments

fdataobj: An fdata object.
nbasis.range: Vector of nbasis values to evaluate (default: 4:20).
type: Basis type: "bspline" (default) or "fourier".
criterion: Selection criterion: "GCV" (default), "CV", "AIC", or "BIC".
kfold: Number of folds for k-fold CV (default 10). Ignored if criterion is "GCV", "AIC", or "BIC".
lambda: Smoothing parameter (default 0).

Value

A list with:

optimal.nbasis: Optimal number of basis functions
scores: Score for each nbasis value
nbasis.range: The tested nbasis values
criterion: The criterion used
fitted: fdata object fitted with optimal nbasis

Examples

set.seed(42)
t <- seq(0, 1, length.out = 50)
X <- matrix(0, 20, 50)
for (i in 1:20) X[i, ] <- sin(4 * pi * t) + rnorm(50, sd = 0.1)
fd <- fdata(X, argvals = t)

# Find optimal nbasis
cv_result <- fdata2basis_cv(fd, nbasis.range = 5:15, type = "fourier")
print(cv_result$optimal.nbasis)
#> [1] 5