The function evaluates the smoothing matrix H, the
matrices Q and S and their associated
coefficients c and s. This function is not intended to be used directly.
dssmoother(X,Y=NULL,lambda,m,s)Returns a list containing the smoothing matrix H, and two
matrices denoted Sgu (for null space) and Qgu.
Matrix of explanatory variables, size n,p.
Vector of response variable. If null, only the smoothing matrix is returned.
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).
Pierre-Andre Cornillon, Nicolas Hengartner and Eric Matzner-Lober
see the reference for detailed explanation of Q (the semi kernel or radial basis) and S (the polynomial null space).
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.
C. Gu (2002) Smoothing spline anova models. New York: Springer-Verlag.
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