iterchoiceAe: Selection of the number of iterations for iterative bias... In ibr: Iterative Bias Reduction

Description

Evaluates at each iteration proposed in the grid the value of different criteria: GCV, AIC, corrected AIC, BIC and gMDL (along with the ddl and sigma squared). The minimum of these criteria gives an estimate of the optimal number of iterations. This function is not intended to be used directly.

Usage

 1 2 iterchoiceAe(Y, K, eigenvaluesA, tPADmdemiY, DdemiPA, ddlmini, ddlmaxi)

Arguments

 Y The response variable. K A numeric vector which give the search grid for iterations. eigenvaluesA Vector of the eigenvalues of the symmetric matrix A. tPADmdemiY 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. DdemiPA The square root of the diagonal matrix D times the eigen vectors of the symmetric matrix A. ddlmini The number of eigenvalues (numerically) which are equal to 1. ddlmaxi The maximum df. No criteria are calculated beyond the number of iterations that leads to df bigger than this bound.

Details

See the reference for detailed explanation of A and D

Value

Returns the values of GCV, AIC, corrected AIC, BIC, gMDL, df and sigma squared for each value of the grid K. Inf are returned if the iteration leads to a smoother with a df bigger than ddlmaxi.

Author(s)

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

References

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.