dssmoother: Evaluate the smoothing matrix, the radial basis matrix, the... In ibr: Iterative Bias Reduction

Description

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.

Usage

 `1` ```dssmoother(X,Y=NULL,lambda,m,s) ```

Arguments

 `X` Matrix of explanatory variables, size n,p. `Y` Vector of response variable. If null, only the smoothing matrix is returned. `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).

Details

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

Value

Returns a list containing the smoothing matrix `H`, and 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.

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