drqssbc: Regression Quantile Smoothing Spline with Constraints
In cobs99: Constrained B-splines -- outdated 1999 version

Description Usage Arguments Details Value Author(s) References See Also Examples

Estimate the B-spline coefficients for a regression quantile smoothing spline with optional constraints, using Ng(1996)'s algorithm.

drqssbc(x, y, w= rep(1,n), pw, knots, degree, Tlambda, constraint,
        n.sub = n1000cut(nrq),
        equal, smaller, greater, gradient, coef, maxiter = 20 * n,
        trace = 1,
        n.equal = nrow(equal), n.smaller = nrow(smaller),
        n.greater = nrow(greater), n.gradient = nrow(gradient),
        nrq = length(x), nl1, neqc, niqc, nvar, nj0,
        tau = 0.5, lam, tmin, kmax, lstart, factor,
        eps = .Machine$double.eps, print.warn)

`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 passed to `l1.design` or `loo.design`.
`knots`	numeric vector of knots for the splines.
`degree`	integer, must be 1 or 2.
`Tlambda`	vector of smoothing parameter values λ; if it is longer than one, an “optimal” value will be selected from these.
`constraint`	see `cobs` (but cannot be abbreviated here).
`n.sub`	integer, not larger than sample size `n`; the default has `n.sub == n` as long as `n` is less than 1000.
`equal,smaller, greater`	3-column matrices specifying the respective constraints. The has 0 zeros if there no constraints of the corresponding kind.
`gradient`	3-column matrix for gradient constraints.
`coef`	numeric vector, the initial guess for the B-spline coefficients.
`maxiter`	upper bound of the number of iteration; default to 20*n.
`trace`	integer or logical indicating the tracing level of the underlying algorithms; not much implemented (due to lack of trace in quantreg ..).
`n.equal,n.smaller,n.greater,n.gradient`	integers, each specifying the corresponding number of constraints.
`nrq`	integer, = n, the number of observations.
`nl1`	integer, number of observations in the l1 norm that correspond to roughness measure (may be zero).
`neqc`	integer giving the number of equations.
`niqc`	integer giving the number of inequality constraints; of the same length as `constraint`.
`nvar`	integer giving the number of equations and constraints.
`nj0`	integer; upper limit for the number of unique tau or lambda solutions.
`tau`	desired quantile level; defaults to 0.5 (median).
`lam`	initial λ value.
`tmin`	smallest value of tau to begin PLP in tau.
`kmax`	integer k_0, the largest effective dimension of the model allowed during PLP in lambda.
`lstart`	number, see `cobs.`
`factor`	number in [1,4], see `cobs`.
`eps`	tolerance used in the fortran code in many different contexts.
`print.warn`	logical indicating if warnings should be printed, when the algorithm seems to have behaved somewhat unexpectedly.

This is an auxiliary function for cobs, possibly interesting on its own. This documentation is currently sparse; read the source code!

a list with components ......

(use the cobs package instead!)

Pin Ng; this help page: Martin Maechler.

Ng, P. (1996) An Algorithm for Quantile Smoothing Splines, Computational Statistics \& Data Analysis 22, 99–118.

The main function cobs and its auxiliary qbsks which calls drqssbc() repeatedly.

set.seed(1243)
x  <- 1:32
fx <- (x-5)*(x-15)^2*(x-21)
y  <- fx + round(rnorm(x,s = 0.25),2)
## FAILS  drqssbc(x,y,nrq=32,lam=1,degree=1,knots=c(1,5,15,32))