dsSx {ibr}

Evaluate the smoothing matrix at any point

Description

The function evaluates the matrix Q and S related to the explanatory variables X at any points. This function is not intended to be used directly.

Usage

dsSx(X,Xetoile,m=2,s=0)

Arguments

X

Matrix of explanatory variables, size n,p.

Xetoile

Matrix of new observations with the same number of variables as X, size m,p.

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).

Details

see the reference for detailed explanation of Q (the semi kernel) and S (the polynomial null space).

Value

Returns a list containing two matrices denoted Sgu (for null space) and Qgu

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.

C. Gu (2002) Smoothing spline anova models. New York: Springer-Verlag.

See Also

ibr