The function evaluates all the features needed for a lowrank spline smoothing. This function is not intended to be used directly.
lrsmoother(x,bs,listvarx,lambda,m,s,rank)Returns a list containing the smoothing matrix eigenvectors and eigenvalues
vectors and values, and one
matrix denoted Rm1U and one smoothobject smoothobject.
Matrix of explanatory variables, size n,p.
The type rank of lowrank splines: tps or ds.
The vector of the names of explanatory variables
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.
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).
The rank of lowrank splines.
Pierre-Andre Cornillon, Nicolas Hengartner and Eric Matzner-Lober
see the reference for detailed explanation of the matrix matrix R^-1U (see reference) and smoothCon for the definition of smoothobject
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.
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