sqr3.fit: Cubic Spline Quantile Regression with L2-Norm Roughness...

In qfa: Quantile-Frequency Analysis (QFA) of Time Series and Spline Quantile Regression (SQR)

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()
)

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())

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

qfa documentation built on March 30, 2026, 5:07 p.m.