qbsks2: Quantile B-Spline with Fixed Knots

Description

Compute B-spline coefficients for regression quantile B-spline with stepwise knots selection and quantile B-spline with fixed knots regression spline, using Ng (1996)'s algorithm.

Usage

qbsks2(x,y,w, pw = 0, knots,nknots, degree,Tlambda, constraint, ptConstr,
       maxiter, trace, nrq, nl1 = 0, neqc, tau, select.lambda,
       ks, do.select,
       knots.add = FALSE, repeat.delete.add = FALSE,
       ic = c("AIC", "BIC", "SIC"),
       give.pseudo.x = TRUE,
       rq.tol = 1e-8, tol.kn = 1e-6, tol.0res = 1e-6, 
       print.mesg = TRUE, print.warn = TRUE, rq.print.warn, nk.start)

Value

a list with components

coef: ..
fidel: ..
k: dimensionality of model fit.
ifl: integer ``flag''; the return code.
icyc: integer of length 2, see cobs.
knots: the vector of inner knots.
nknots: the number of inner knots.
nvar: the number of ``variables'', i.e. unknowns including constraints.
lambda: the penalty factor, chosen or given.
pseudo.x: the pseudo design matrix \(X\), as returned from drqssbc2.

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; typically should be 0 here.
knots: numeric vector of knots of which nknots will be used.
nknots: number of knots to be used.

degree: integer specifying polynomial degree; must be 1 or 2.
Tlambda: (vector of) smoothing parameter(s) \(\lambda\), see drqssbc2.
constraint: string (or empty) specifying the global constraints; see cobs.
ptConstr: list of pointwise constraints.
maxiter: non-negative integer: maximal number of iterations, passed to drqssbc2.
trace: integer or logical indicating the tracing level of the underlying algorithms; not implemented (due to lack of trace in quantreg ...)
nrq, nl1, neqc: integers specifying dimensionalities, directly passed to drqssbc2, see there.
tau: desired quantile level (in interval \((0,1)\)).
select.lambda: passed to drqssbc2, see there.
ks: number used as offset in SIC/AIC/BIC.
do.select: logical indicating if knots shall be selected (instead of used as specified).
knots.add, repeat.delete.add: logicals, see cobs.
ic: information criterion to use, see cobs.
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().
tol.kn: “tolerance” for shifting the outer knots.
tol.0res: tolerance passed to drqssbc2.
print.mesg: an integer indicating how qbsks2() should print message about its current stages.
print.warn: flag indicating if and how much warnings and information is to be printed; currently just passed to drqssbc2.
rq.print.warn: flag for quantreg's fitting functions, just passed to drqssbc2.
nk.start: number of starting knots used in automatic knot selection.

Author

Pin Ng; this help page: Martin Maechler.

Details

This is an auxiliary function for cobs(*, lambda = 0), possibly interesting on its own. This documentation is currently sparse; read the source code!

References

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