qss {nprq}R Documentation

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, 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","U","C" "UI","UD","CI","CD" for none, increasing, decreasing, convex, concave, convex and increasing, etc. And for bivariate qss components can take the values "N","U","C" for none, convex, and concave.
w weights not yet unimplemented

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.

Value

F Fidelity component of the design matrix
A Penalty component of the design matrix
R Constraint component of the design matrix
r Constraint component of the rhs

Author(s)

Roger Koenker

See Also

rqss


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