minmaxBias {ROptEst}R Documentation

Generic Function for the Computation of Bias-Optimally Robust ICs

Description

Generic function for the computation of bias-optimally robust ICs in case of infinitesimal robust models. This function is rarely called directly.

Usage

minmaxBias(L2deriv, neighbor, biastype, ...)

## S4 method for signature 'UnivariateDistribution,
##   ContNeighborhood, BiasType':
minmaxBias(L2deriv, neighbor, biastype, symm, trafo, 
             maxiter, tol, warn, Finfo)

## S4 method for signature 'UnivariateDistribution,
##   ContNeighborhood, asymmetricBias':
minmaxBias(L2deriv, neighbor, biastype, symm, trafo, 
             maxiter, tol, warn, Finfo)

## S4 method for signature 'UnivariateDistribution,
##   ContNeighborhood, onesidedBias':
minmaxBias(L2deriv, neighbor, biastype, symm, trafo, 
             maxiter, tol, warn, Finfo)

## S4 method for signature 'UnivariateDistribution,
##   TotalVarNeighborhood, BiasType':
minmaxBias(L2deriv, neighbor, biastype, symm, trafo, 
             maxiter, tol, warn, Finfo)

## S4 method for signature 'RealRandVariable,
##   ContNeighborhood, BiasType':
minmaxBias(L2deriv, neighbor, biastype, normtype, Distr, 
             z.start, A.start,  z.comp, A.comp, trafo, maxiter, tol)

Arguments

L2deriv L2-derivative of some L2-differentiable family of probability measures.
neighbor object of class "Neighborhood".
biastype object of class "BiasType".
normtype object of class "NormType".
... additional parameters.
Distr object of class "Distribution".
symm logical: indicating symmetry of L2deriv.
z.start initial value for the centering constant.
A.start initial value for the standardizing matrix.
z.comp logical indicator which indices need to be computed and which are 0 due to symmetry.
A.comp matrix of logical indicator which indices need to be computed and which are 0 due to symmetry.
trafo matrix: transformation of the parameter.
maxiter the maximum number of iterations.
tol the desired accuracy (convergence tolerance).
warn logical: print warnings.
Finfo Fisher information matrix.

Value

The bias-optimally robust IC is computed.

Methods

L2deriv = "UnivariateDistribution", neighbor = "ContNeighborhood", biastype = "BiasType"
computes the bias optimal influence curve for symmetric bias for L2 differentiable parametric families with unknown one-dimensional parameter.
L2deriv = "UnivariateDistribution", neighbor = "ContNeighborhood", biastype = "asymmetricBias"
computes the bias optimal influence curve for asymmetric bias for L2 differentiable parametric families with unknown one-dimensional parameter.
L2deriv = "UnivariateDistribution", neighbor = "TotalVarNeighborhood", biastype = "BiasType"
computes the bias optimal influence curve for symmetric bias for L2 differentiable parametric families with unknown one-dimensional parameter.
L2deriv = "RealRandVariable", neighbor = "ContNeighborhood", biastype = "BiasType"
computes the bias optimal influence curve for symmetric bias for L2 differentiable parametric families with unknown k-dimensional parameter (k > 1) where the underlying distribution is univariate.

Author(s)

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

References

Rieder, H. (1980) Estimates derived from robust tests. Ann. Stats. 8: 106–115.

Rieder, H. (1994) Robust Asymptotic Statistics. New York: Springer.

Ruckdeschel, P. (2005) Optimally One-Sided Bounded Influence Curves. Mathematical Methods in Statistics 14(1), 105-131.

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

See Also

InfRobModel-class


[Package ROptEst version 0.6.3 Index]