radiusMinimaxIC {ROptEst}R Documentation

Generic function for the computation of the radius minimax IC

Description

Generic function for the computation of the radius minimax IC.

Usage

radiusMinimaxIC(L2Fam, neighbor, risk, ...)

## S4 method for signature 'L2ParamFamily,
##   UncondNeighborhood, asGRisk':
radiusMinimaxIC(
        L2Fam, neighbor, risk, loRad, upRad, z.start = NULL, A.start = NULL, 
        upper = 1e5, maxiter = 50, tol = .Machine$double.eps^0.4, 
        warn = FALSE, verbose = FALSE)

Arguments

L2Fam L2-differentiable family of probability measures.
neighbor object of class "Neighborhood".
risk object of class "RiskType".
... additional parameters.
loRad the lower end point of the interval to be searched.
upRad the upper end point of the interval to be searched.
z.start initial value for the centering constant.
A.start initial value for the standardizing matrix.
upper upper bound for the optimal clipping bound.
maxiter the maximum number of iterations
tol the desired accuracy (convergence tolerance).
warn logical: print warnings.
verbose logical: if TRUE, some messages are printed

Details

In case the neighborhood radius is unknown, Rieder et al. (2001, 2008) and Kohl (2005) show that there is nevertheless a way to compute an optimally robust IC - the so-called radius-minimax IC - which is optimal for some radius interval.

Value

The radius minimax IC is computed.

Methods

L2Fam = "L2ParamFamily", neighbor = "UncondNeighborhood", risk = "asGRisk":
computation of the radius minimax IC for an L2 differentiable parametric family.

Author(s)

Matthias Kohl Matthias.Kohl@stamats.de, Peter Ruckdeschel Peter.Ruckdeschel@itwm.fraunhofer.de

References

Rieder, H., Kohl, M. and Ruckdeschel, P. (2008) The Costs of not Knowing the Radius. Statistical Methods and Applications, 17(1) 13-40.

Rieder, H., Kohl, M. and Ruckdeschel, P. (2001) The Costs of not Knowing the Radius. Appeared as discussion paper Nr. 81. SFB 373 (Quantification and Simulation of Economic Processes), Humboldt University, Berlin; also available under www.uni-bayreuth.de/departments/math/org/mathe7/RIEDER/pubs/RR.pdf

Kohl, M. (2005) Numerical Contributions to the Asymptotic Theory of Robustness. Bayreuth: Dissertation.

See Also

radiusMinimaxIC

Examples

N <- NormLocationFamily(mean=0, sd=1) 
radIC <- radiusMinimaxIC(L2Fam=N, neighbor=ContNeighborhood(), 
                         risk=asMSE(), loRad=0.1, upRad=0.5)
checkIC(radIC)

[Package ROptEst version 0.6.3 Index]