qbsks: Quantile B-Spline with Fixed Knots

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

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, knots,nknots, degree,Tlambda, constraint, ptConstr,
      maxiter, trace, nrq,nl1, neqc, tau, select.lambda,
      ks, do.select, knots.add, repeat.delete.add, ic, print.mesg,
      give.pseudo.x = TRUE,
      rq.tol = 1e-8, tol.kn = 1e-6, tol.0res = 1e-6, print.warn, nk.start)

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 ... ...
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.
print.mesg	an integer indicating how qbsks2() should print message about its current stages.
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.warn	flag indicating if and how much warnings and information is to be printed; currently just passed to drqssbc2.
nk.start	number of starting knots used in automatic knot selection.

Details

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

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.

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 references in cobs.

See Also

the main function cobs; further drqssbc2 which is called from qbsks2().

cobs documentation built on May 29, 2024, 11:02 a.m.