cobs: drqssbc – R documentation

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drqssbc

Regression Quantile Smoothing Spline with Constraints

Description

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

Usage

drqssbc2(x, y, w = rep.int(1,n), pw, knots, degree, Tlambda,
        constraint, ptConstr, maxiter = 100, trace = 0,
        nrq = length(x), nl1, neqc, niqc, nvar,
        tau = 0.5, select.lambda, give.pseudo.x = FALSE,
        rq.tol = 1e-8 * sc.y, tol.0res = 1e-6,
        print.warn = TRUE, rq.print.warn = FALSE)

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 passed to `l1.design2` or `loo.design2`. FIXME: This is currently unused.
`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).
`ptConstr`	`list` of pointwise constraints; notably `equal`, `smaller`, `greater` and `gradient` are 3-column matrices specifying the respective constraints. May have 0 rows if there are no constraints of the corresponding kind.
`maxiter`	maximal number of iterations; defaults to 100.
`trace`	integer or logical indicating the tracing level of the underlying algorithms; not much implemented (due to lack of trace in quantreg ...)
`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.
`tau`	desired quantile level; defaults to 0.5 (median).
`select.lambda`	logical indicating if an optimal lambda should be selected from the vector of `Tlambda`.
`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()`. Note that (for scale invariance) this has to be in units of `y`, which the default makes use of.
`tol.0res`	tolerance used to check for zero residuals, i.e., \|r_i\| < tol mean(\|r_i\|)*.
`print.warn`	logical indicating if warnings should be printed, when the algorithm seems to have behaved somewhat unexpectedly.
`rq.print.warn`	logical indicating if warnings should be printed from inside the `rq.*` function calls, see below.

Details

This is an auxiliary function for cobs, possibly interesting on its own. Depending on degree, either l1.design2 or loo.design2 are called for construction of the sparse design matrix.

Subsequently, either rq.fit.sfnc or rq.fit.sfn is called as the main “work horse”.

This documentation is currently sparse; read the source code!

Value

a list with components

`comp1`	Description of ‘comp1’
`comp2`	Description of ‘comp2’

...

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.

Examples

set.seed(1243)
x  <- 1:32
fx <- (x-5)*(x-15)^2*(x-21)
y  <- fx + round(rnorm(x,s = 0.25),2)

cobs

Constrained B-Splines (Sparse Matrix Based)

v1.3-4

GPL (>= 2)

Authors

Pin T. Ng <Pin.Ng@nau.edu> and Martin Maechler

Initial release

2020-01-20