R: Quantile B-Spline with Fixed Knots

qbsks2 {cobs} | R Documentation

## 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) λ, 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 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()`.

[Package cobs version 1.3-3 Index]