betaS1lr: Coefficients for iterative bias reduction method.

Description Usage Arguments Details Value Author(s) References See Also

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
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.

See Also

ibr


ibr documentation built on May 2, 2019, 8:22 a.m.