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.
betaS1(n,U,tUy,eigenvaluesS1,ddlmini,k,lambda,Sgu,Qgu,index0)Returns a list containing of coefficients for the null space dgub
and the semi-kernel cgub
The number of observations.
The the matrix of eigen vectors of the symmetric smoothing matrix S.
The transpose of the matrix of eigen vectors of the symmetric smoothing matrix S times the vector of observation y.
Vector of the eigenvalues of the symmetric smoothing matrix S.
The number of eigen values of S equal to 1.
A numeric vector which give the number of iterations.
The smoothness coefficient lambda for thin plate splines of
order m.
The matrix of the polynomial null space S.
The matrix of the semi kernel (or radial basis) Q.
The index of the first eigen values of S numerically equal to 0.
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).
C. Gu (2002) Smoothing spline anova models. New York: Springer-Verlag.
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