Calculates the coefficients for the iterative bias reduction smoothers. This function is not intended to be used directly.
betaA(n, eigenvaluesA, tPADmdemiY, DdemiPA, ddlmini, k, index0)Returns the vector of coefficients (of length n, the number of observations.)
The number of observations.
Vector of the eigenvalues of the symmetric matrix A.
The transpose of the matrix of eigen vectors of the symmetric matrix A times the inverse of the square root of the diagonal matrix D.
The square root of the diagonal matrix D times the eigen vectors of the symmetric matrix A.
The number of eigenvalues (numerically) equals to 1.
A scalar which gives the number of iterations.
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 A and D and the meaning of coefficients.
Cornillon, P.-A.; Hengartner, N.; Jegou, N. and Matzner-Lober, E. (2012) Iterative bias reduction: a comparative study. Statistics and Computing, 23, 777-791.
Cornillon, P.-A.; Hengartner, N. and Matzner-Lober, E. (2013) Recursive bias estimation for multivariate regression smoothers Recursive bias estimation for multivariate regression smoothers. ESAIM: Probability and Statistics, 18, 483-502.
Cornillon, P.-A.; Hengartner, N. and Matzner-Lober, E. (2017) Iterative Bias Reduction Multivariate Smoothing in R: The ibr Package. Journal of Statistical Software, 77, 1--26.
ibr