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ibr (version 2.0-2)

lrsmoother: 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.

Value

vectors and values, and one matrix denoted Rm1U and one smoothobject smoothobject.

Details

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

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