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) `\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.