iterchoiceA: Selection of the number of iterations for iterative bias...

In ibr: Iterative Bias Reduction

Selection of the number of iterations for iterative bias reduction smoothers

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 stats::optimize. This function is not intended to be used directly.

Usage

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 stats::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.

See Also

ibr, iterchoiceA

ibr documentation built on Sept. 12, 2025, 10:19 a.m.