lrsmoother {ibr} | R Documentation |
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: |
listvarx |
The vector of the names of explanatory variables |
lambda |
The smoothness coefficient lambda for thin plate splines of
order |
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.