cobs (version 1.3-7)

# 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, knots,nknots, degree,Tlambda, constraint, ptConstr,
maxiter, trace, nrq,nl1, neqc, tau, select.lambda,
give.pseudo.x = TRUE,
rq.tol = 1e-8, tol.kn = 1e-6, tol.0res = 1e-6, 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 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).

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.

## 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.

See also the references in cobs.

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