sqr.fit: Cubic Spline Quantile Regression with L1-Norm Roughness...

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

Cubic Spline Quantile Regression with L1-Norm Roughness Penalty (SQR)

Description

This function computes spline quantile regression solution with cubic splines and L1-norm roughness penalty (SQR) from the response vector and the design matrix on a given set of quantile levels. It uses the FORTRAN code rqfnb.f in the "quantreg" package with the kind permission of Dr. R. Koenker or the R function rq.fit.sfn() in the same package as a sparse-matrix alternative. Both solve the SQR problem as a linear program (LP).

Usage

sqr.fit(
  X,
  y,
  tau,
  tau0 = tau,
  spar = 1,
  w = rep(1, length(tau0)),
  mthreads = TRUE,
  ztol = 1e-05,
  solver = c("fnb", "sfn"),
  all.knots = FALSE
)

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, set RhpcBLASctl::blas_set_num_threads(1) (default = TRUE)
ztol	zero-tolerance parameter to determine the model complexity (default = 1e-05)
solver	LP solver: 'fnb' (defaut) or 'sfn'
all.knots	TRUE or FALSE (default), same as in smooth.spline()

Value

A list with the following elements:

coefficients	matrix of regression coefficients
derivatives	matrix of derivatives of regression coefficients
crit	criteria values for spar selection: (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.