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)
```

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`

.

- 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.

Pin Ng; this help page: Martin Maechler.

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()`

.