sqr3.fit: Cubic Spline Quantile Regression with L2-Norm Roughness Penalty (SQR3 or Cubic SQR)

Description

This function computes spline quantile regression with cubic splines and L2-norm roughness penalty (SQR3 or cubic SQR) from the response vector and the design matrix on a given set of quantile levels. It uses solve_osqp() in the "osqp" package or solve_piqp() in the "piqp" package. Both are general-purpose quadratic program (QP) solvers in the sparse-matrix form.

Usage

sqr3.fit(
  X,
  y,
  tau,
  tau0 = tau,
  spar = 1,
  w = rep(1, length(tau0)),
  mthreads = FALSE,
  ztol = 1e-04,
  type = c("dual", "primal"),
  solver = c("piqp", "osqp"),
  npar = c(1, 2),
  all.knots = FALSE,
  control = list()
)

Value

A list with the following elements:

coefficients: matrix of regression coefficients
derivatives: matrix of derivatives of regression coefficients
crit: sequence critera for smoothing parameter select: (AIC,BIC,GIC)
np: sequence of complexity measure as the number of effective parameters
fid: sequence of fidelity measure as the quasi-likelihood
info: convergence status
nit: number of iterations
K: number of spline basis functions

Arguments

X: design matrix (requirement: nrow(X) = length(y))
y: response vector
tau: sequence of quantile levels for evaluation
tau0: sequence of quantile levels for fitting (min(tau0) <= tau <= max(tau0); default = tau)
spar: smoothing parameter (default = 1)
w: weight sequence in penalty (default = rep(1,length(tau0)))
mthreads: if FALSE (default), set RhpcBLASctl::blas_set_num_threads(1)
ztol: zero-tolerance parameter to determine the model complexity (default = 1e-04)
type: type of QP formulation: 'dual' (default) or 'primal'
solver: QP solver: 'piqp' (default) or 'osqp'
npar: experimental parameter (default = 1)
all.knots: TRUE or FALSE (default) as in stats::smooth.spline()
control: list of control parameters for the QP solver (default = list())