make_matrices_dens function

Build a standardised P-Spline design matrix and the associated P-Spline penalty matrix

This function builds the B-spline design matrix for a given data vector. Importantly, the B-spline basis functions are normalised such that the integral of each basis function is 1, hence this basis can be used for spline-based density estimation, when the basis functions are weighted by non-negative weights summing to one.

make_matrices_dens(
  x,
  k,
  type = "real",
  degree = 3,
  npoints = 10000,
  diff_order = 2,
  pow = 0.5
)

Arguments

• x: data vector

• k: number of basis functions

• type: type of the data, either "real" for data on the reals, "positive" for data on the positive reals or "circular" for circular data like angles.

• degree: degree of the B-spline basis functions, defaults to cubic B-splines

• npoints: number of points used in the numerical integration for normalizing the B-spline basis functions

• diff_order: order of differencing used for the P-Spline penalty matrix for each data stream. Defaults to second-order differences.

• pow: power for polynomial knot spacing

  Such non-equidistant knot spacing is only used for type = "positive".

Returns

list containing the design matrix Z, the penalty matrix S, the prediction design matrix Z_predict, the prediction grid xseq, and details for the basis expansion.

Examples

modmat = make_matrices_dens(x = (-50):50, k = 20)
modmat = make_matrices_dens(x = 1:100, k = 20, type = "positive")
modmat = make_matrices_dens(x = seq(-pi,pi), k = 20, type = "circular")