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

Description

The function iterchoiceA searches the interval from mini to maxi for a minimum of the function which calculates the chosen criterion (critAgcv, critAaic, critAbic, critAaicc or critAgmdl) with respect to its first argument (a given iteration k) using optimize. This function is not intended to be used directly.

Usage

 1 2 iterchoiceA(n, mini, maxi, eigenvaluesA, tPADmdemiY, DdemiPA, ddlmini, ddlmaxi, y, criterion, fraction)

Arguments

 n The number of observations. mini The lower end point of the interval to be searched. maxi The upper end point of the interval to be searched. 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) equals to 1. ddlmaxi The maximum df. No criterion is calculated and Inf is returned. y The vector of observations of dependant variable. criterion The criteria available are GCV (default, "gcv"), AIC ("aic"), corrected AIC ("aicc"), BIC ("bic") or gMDL ("gmdl"). fraction The subdivision of the interval [mini,maxi].

Details

See the reference for detailed explanation of A and D. The interval [mini,maxi] is splitted into subintervals using fraction. In each subinterval the function fcriterion is minimzed using optimize (with respect to its first argument) and the minimum (and its argument) of the result of these optimizations is returned.

Value

A list with components iter and objective which give the (rounded) optimum number of iterations (between Kmin and Kmax) and the value of the function at that real point (not rounded).

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.