drqssbc: Regression Quantile Smoothing Spline with Constraints

In cobs: Constrained B-Splines (Sparse Matrix Based)

Regression Quantile Smoothing Spline with Constraints

Description

Estimate the B-spline coefficients for a regression quantile smoothing spline with optional constraints, using Ng(1996)'s algorithm.

Usage

drqssbc2(x, y, w = rep.int(1,n), pw, knots, degree, Tlambda,
        constraint, ptConstr, maxiter = 100, trace = 0,
        nrq = length(x), nl1, neqc, niqc, nvar,
        tau = 0.5, select.lambda, give.pseudo.x = FALSE,
        rq.tol = 1e-8 * sc.y, tol.0res = 1e-6,
        print.warn = TRUE, rq.print.warn = trace >= 2)

Arguments

x	numeric vector, sorted increasingly, the abscissa values
y	numeric, same length as x, the observations.
w	numeric vector of weights, same length as x, as in cobs.
pw	penalty weights vector passed to l1.design2 or loo.design2. FIXME: This is currently unused.
knots	numeric vector of knots for the splines.
degree	integer, must be 1 or 2.
Tlambda	vector of smoothing parameter values \lambda; if it is longer than one, an “optimal” value will be selected from these.
constraint	see cobs (but cannot be abbreviated here).
ptConstr	list of pointwise constraints; notably equal, smaller, greater and gradient are 3-column matrices specifying the respective constraints. May have 0 rows if there are no constraints of the corresponding kind.
maxiter	maximal number of iterations; defaults to 100.
trace	integer or logical indicating the tracing level of the underlying algorithms; not much implemented (due to lack of trace in quantreg ...)
nrq	integer, = n, the number of observations.
nl1	integer, number of observations in the l1 norm that correspond to roughness measure (may be zero).
neqc	integer giving the number of equations.
niqc	integer giving the number of inequality constraints; of the same length as constraint.
nvar	integer giving the number of equations and constraints.
tau	desired quantile level; defaults to 0.5 (median).
select.lambda	logical indicating if an optimal lambda should be selected from the vector of Tlambda.
give.pseudo.x	logical indicating if the pseudo design matrix \tilde{X} should be returned (as sparse matrix).
rq.tol	numeric convergence tolerance for the interior point algorithm called from rq.fit.sfnc() or rq.fit.sfn(). Note that (for scale invariance) this has to be in units of y, which the default makes use of.
tol.0res	tolerance used to check for zero residuals, i.e., |r_i| < tol * mean(|r_i|).
print.warn	logical indicating if warnings should be printed, when the algorithm seems to have behaved somewhat unexpectedly.
rq.print.warn	logical indicating if warnings should be printed from inside the rq.* function calls, see below.

Details

This is an auxiliary function for cobs, possibly interesting on its own. Depending on degree, either l1.design2 or loo.design2 are called for construction of the sparse design matrix.

Subsequently, either rq.fit.sfnc or rq.fit.sfn is called as the main “work horse”.

This documentation is currently sparse; read the source code!

Value

a list with components

comp1	Description of ‘comp1’
comp2	Description of ‘comp2’

...

Author(s)

Pin Ng; this help page: Martin Maechler.

References

Ng, P. (1996) An Algorithm for Quantile Smoothing Splines, Computational Statistics & Data Analysis 22, 99–118.

See Also

The main function cobs and its auxiliary qbsks2 which calls drqssbc2() repeatedly.

l1.design2 and loo.design2; further rq.fit.sfnc and rq.fit.sfn from package quantreg.

Examples

set.seed(1243)
x  <- 1:32
fx <- (x-5)*(x-15)^2*(x-21)
y  <- fx + round(rnorm(x,s = 0.25),2)

cobs documentation built on June 30, 2025, 3:01 p.m.