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

Usage

iterchoiceA(n, mini, maxi, eigenvaluesA, tPADmdemiY, DdemiPA, 
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.

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.

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

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.

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.