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.

```
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)
```

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 **p**oin**t**wise 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.

a list with components

..

..

dimensionality of model fit.

integer ``flag''; the return code.

integer of length 2, see `cobs`

.

the vector of inner knots.

the number of inner knots.

the number of ``variables'', i.e. unknowns including constraints.

the penalty factor, chosen or given.

the pseudo design matrix \(X\), as returned from
`drqssbc2`

.

This is an auxiliary function for `cobs(*, lambda = 0)`

,
possibly interesting on its own. This documentation is currently sparse; read
the source code!

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()`

.