betaS1: Coefficients for iterative bias reduction method.

In ibr: Iterative Bias Reduction

Coefficients for iterative bias reduction method.

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

betaS1(n,U,tUy,eigenvaluesS1,ddlmini,k,lambda,Sgu,Qgu,index0)

Arguments

n	The number of observations.
U	The the matrix of eigen vectors of the symmetric smoothing matrix S.
tUy	The transpose of the matrix of eigen vectors of the symmetric smoothing matrix S times the vector of observation y.
eigenvaluesS1	Vector of the eigenvalues of the symmetric smoothing matrix S.
ddlmini	The number of eigen values of S equal to 1.
k	A numeric vector which give the number of iterations.
lambda	The smoothness coefficient lambda for thin plate splines of order m.
Sgu	The matrix of the polynomial null space S.
Qgu	The matrix of the semi kernel (or radial basis) Q.
index0	The index of the first eigen values of S numerically equal to 0.

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 of coefficients for the null space dgub and the semi-kernel cgub

Author(s)

Pierre-Andre Cornillon, Nicolas Hengartner and Eric Matzner-Lober

References

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

See Also

ibr

ibr documentation built on Sept. 12, 2025, 10:19 a.m.