P-spline Smoothing for Functional Data

Fits penalized B-splines (P-splines) to functional data with automatic or manual selection of the smoothing parameter.

Usage

pspline(
  fdataobj,
  nbasis = 20,
  lambda = 1,
  order = 2,
  lambda.select = FALSE,
  criterion = c("GCV", "AIC", "BIC"),
  lambda.range = 10^seq(-4, 4, length.out = 50)
)

Arguments

fdataobj: An fdata object.
nbasis: Number of B-spline basis functions (default 20).
lambda: Smoothing parameter. Higher values give smoother curves. If NULL and lambda.select = TRUE, selected automatically.
order: Order of the difference penalty (default 2, for second derivative penalty).
lambda.select: Logical. If TRUE, select lambda automatically using the specified criterion.
criterion: Criterion for lambda selection: "GCV" (default), "AIC", or "BIC".
lambda.range: Range of lambda values to search (log10 scale). Default: 10^seq(-4, 4, length.out = 50).

Value

A list of class "pspline" with:

fdata: Smoothed fdata object
coefs: Coefficient matrix
lambda: Used or selected lambda value
edf: Effective degrees of freedom
gcv/aic/bic: Criterion values
nbasis: Number of basis functions used

Details

P-splines minimize: $$||y - B c||^2 + \lambda c' D' D c$$ where B is the B-spline basis matrix, c are coefficients, and D is the difference matrix of the specified order.

References

Eilers, P.H.C. and Marx, B.D. (1996). Flexible smoothing with B-splines and penalties. Statistical Science, 11(2), 89-121.

Examples

# Create noisy data
t <- seq(0, 1, length.out = 100)
true_signal <- sin(2 * pi * t)
noisy <- true_signal + rnorm(100, sd = 0.3)
fd <- fdata(matrix(noisy, nrow = 1), argvals = t)

# Smooth with P-splines
result <- pspline(fd, nbasis = 20, lambda = 10)
plot(fd)

lines(t, result$fdata$data[1, ], col = "red", lwd = 2)
#> Error in plot.xy(xy.coords(x, y), type = type, ...): plot.new has not been called yet

# Automatic lambda selection
result_auto <- pspline(fd, nbasis = 20, lambda.select = TRUE)