iterchoiceS1: Number of iterations selection for iterative bias reduction model

Description

The function iterchoiceS1 searches the interval from mini to maxi for a minimum of the function which calculates the chosen criterion (critS1gcv, critS1aic, critS1bic, critS1aicc or critS1gmdl) with respect to its first argument (a given iteration k) using optimize. This function is not intended to be used directly.

Usage

iterchoiceS1(n, mini, maxi, tUy, eigenvaluesS1, ddlmini, ddlmaxi,
y, criterion, fraction)

Arguments

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.

eigenvaluesS1

Vector of the eigenvalues 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.

ddlmini

The number of eigen values of S equal to 1.

ddlmaxi

The maximum df. No criterion is calculated and Inf is returned.

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].

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).

Details

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.

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.