lrsmoother: Evaluate the lowrank spline

In ibr: Iterative Bias Reduction

Evaluate the lowrank spline

Description

The function evaluates all the features needed for a lowrank spline smoothing. This function is not intended to be used directly.

Usage

lrsmoother(x,bs,listvarx,lambda,m,s,rank)

Arguments

x	Matrix of explanatory variables, size n,p.
bs	The type rank of lowrank splines: tps or ds.
listvarx	The vector of the names of explanatory variables
lambda	The smoothness coefficient lambda for thin plate splines of order m.
m	The order of derivatives for the penalty (for thin plate splines it is the order). This integer m must verify 2m+2s/d>1, where d is the number of explanatory variables.
s	The power of weighting function. For thin plate splines s is equal to 0. This real must be strictly smaller than d/2 (where d is the number of explanatory variables) and must verify 2m+2s/d. To get pseudo-cubic splines, choose m=2 and s=(d-1)/2 (See Duchon, 1977).
rank	The rank of lowrank splines.

Details

see the reference for detailed explanation of the matrix matrix R^-1U (see reference) and smoothCon for the definition of smoothobject

Value

Returns a list containing the smoothing matrix eigenvectors and eigenvalues vectors and values, and one matrix denoted Rm1U and one smoothobject smoothobject.

Author(s)

Pierre-Andre Cornillon, Nicolas Hengartner and Eric Matzner-Lober

References

Duchon, J. (1977) Splines minimizing rotation-invariant semi-norms in Solobev spaces. in W. Shemp and K. Zeller (eds) Construction theory of functions of several variables, 85-100, Springer, Berlin.

Wood, S.N. (2003) Thin plate regression splines. J. R. Statist. Soc. B, 65, 95-114.

See Also

ibr

ibr documentation built on Sept. 13, 2023, 5:08 p.m.