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quantreg (version 4.77)

qss: Additive Nonparametric Terms for rqss Fitting

Description

In the formula specification of rqss nonparametric terms are specified with qss. Both univariate and bivariate specifications are possible, and qualitative constraints may also be specified for the qss terms.

Usage

qss(x, constraint = "N", lambda = 1, ndum = 0, dummies = NULL, w = rep(1, length(x)))

Arguments

x
The covariate determining the nonparametric component, if x is a matrix with two columns then the qss function will construct a penalized triogram term.
lambda
The smoothing parameter governing the tradeoff between fidelity and the penalty component for this term. In future versions there should be an automatic mechanism for default choice of the lambdas. For now, this is the responsibility of the user.
constraint
Optional specification of qualitative constraints on the fitted univariate qss functions, take the values: "N","I","D","V","C" "VI","VD","CI","CD" for none, increasing, decreasing, convex, concave, convex and increasing, etc. And for bivariate qss co
ndum
number of dummy vertices: this is only relevant for qss2 terms. In addition to vertices at the observed (x,y) points ndum dummy vertices are generated -- distributed uniformly over the rectangle given by the Cartesian product of the ranges of x and y
dummies
list of dummy vertices as generated, for example by triogram.fidelity when ndum > 0. Should be a list with x and y components. These points should lie inside the convex hull of the real xy points, but no explicit checking of this assertion is curren
w
weights not yet unimplemented

Value

  • FFidelity component of the design matrix
  • dummiesList of dummy vertices
  • APenalty component of the design matrix
  • RConstraint component of the design matrix
  • rConstraint component of the rhs

Details

The various pieces returned are stored in sparse matrix.csr form. See rqss for details on how they are assembled. To preserve the sparsity of the design matrix the first column of each qss term is dropped. This differs from the usual convention that would have forced qss terms to have mean zero. This convention has implications for prediction that need to be recognized. The penalty components for qss terms are based on total variation penalization of the first derivative (and gradient, for bivariate x) as described in the references appearing in the help for rqss.

For the bivariate case, package tripack (and for plotting also akima) are required (automatically, by the Rcode).

See Also

rqss