wridge_solver function

Fit B-Splines with weighted penalization over differences of parameters

wridge_solver(
  XX_band,
  Xy,
  degree,
  pen,
  w = rep(1, nrow(XX_band) - degree - 1),
  old_par = rep(1, nrow(XX_band)),
  maxiter = 1000,
  tol = 1e-08
)

Arguments

• XX_band: The matrix $X^T X$ where X is the design matrix. This argument is given in the form of a band matrix, i.e., successive columns represent superdiagonals.
• Xy: The vector of currently estimated points $X^T y$, where y is the y-coordinate of the data.
• degree: The degree of the B-splines.
• pen: Positive penalty constant.
• w: Vector of weights. The case $\mathbf w = \mathbf 1$ corresponds to fitting P-splines with difference #' order degree + 1 (see Eilers, P., Marx, B. (1996) Flexible smoothing with B-splines and penalties.)
• old_par: Initial parameter to serve as starting point of the iterating process.
• maxiter: Maximum number of Newton-Raphson iterations to be computed.
• tol: The tolerance chosen to diagnostic convergence of the adaptive ridge procedure.

Returns

The estimated parameter of the spline regression.