R: Coefficients for iterative bias reduction method.

betaS1lr {ibr}

R Documentation

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

betaS1lr(n,U,tUy,eigenvaluesS1,ddlmini,k,lambda,rank,Rm1U,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`.
`rank`	The rank of lowrank splines.
`Rm1U`	matrix R^-1U (see reference).
`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 beta

Author(s)

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

References

Wood, S.N. (2003) Thin plate regression splines. J. R. Statist. Soc. B, 65, 95-114.