Automatic basis selection for each curve individually.

This function compares Fourier and P-spline bases for each curve, selecting the optimal basis type and number of basis functions using model selection criteria (GCV, AIC, or BIC).

Usage

select_basis_auto(
  data,
  argvals,
  criterion,
  nbasis_min,
  nbasis_max,
  lambda_pspline,
  use_seasonal_hint
)

Arguments

• data - Functional data matrix (n x m)

• argvals - Evaluation points

• criterion - Model selection criterion: 0=GCV (default), 1=AIC, 2=BIC

• nbasis_min - Minimum number of basis functions (0 for auto)

• nbasis_max - Maximum number of basis functions (0 for auto)

• lambda_pspline - Smoothing parameter for P-spline (negative for auto-select)

• use_seasonal_hint - Whether to use FFT to detect seasonality

Returns

Named list with:

• basis_type: Integer vector (0=pspline, 1=fourier)

• nbasis: Integer vector of selected nbasis per curve

• score: Numeric vector of criterion scores

• coefficients: List of coefficient vectors

• fitted: Fitted values matrix (n x m)

• edf: Numeric vector of effective degrees of freedom

• seasonal_detected: Logical vector

• lambda: Numeric vector of lambda values (NA for Fourier)

• criterion: Character (criterion name used)