minmaxBias: 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 UnivariateDistribution,ContNeighborhood,BiasType
minmaxBias(L2deriv,
     neighbor, biastype, symm, trafo, maxiter, tol, warn, Finfo, verbose = NULL)
# S4 method for UnivariateDistribution,ContNeighborhood,asymmetricBias
minmaxBias(
     L2deriv, neighbor, biastype, symm, trafo, maxiter, tol, warn, Finfo, verbose = NULL)
# S4 method for UnivariateDistribution,ContNeighborhood,onesidedBias
minmaxBias(
     L2deriv, neighbor, biastype, symm, trafo, maxiter, tol, warn, Finfo, verbose = NULL)
# S4 method for UnivariateDistribution,TotalVarNeighborhood,BiasType
minmaxBias(
     L2deriv, neighbor, biastype, symm, trafo, maxiter, tol, warn, Finfo, verbose = NULL)
# S4 method for RealRandVariable,ContNeighborhood,BiasType
minmaxBias(L2deriv,
     neighbor, biastype, normtype, Distr, z.start, A.start,  z.comp, A.comp,
     Finfo, trafo, maxiter, tol, verbose = NULL, ...)
# S4 method for RealRandVariable,TotalVarNeighborhood,BiasType
minmaxBias(L2deriv,
     neighbor, biastype, normtype, Distr, z.start, A.start,  z.comp, A.comp,
     Finfo, trafo, maxiter, tol, verbose = NULL, ...)

Value

The bias-optimally robust IC is computed.

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 arguments to be passed to E
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.
verbose: logical: if TRUE, some messages are printed

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.
L2deriv = "RealRandVariable", neighbor = "TotalNeighborhood", biastype = "BiasType": computes the bias optimal influence curve for symmetric bias for L2 differentiable parametric families in a setting where we are interested in a \(p=1\) dimensional aspect of an unknown \(k\)-dimensional parameter (\(k > 1\)) where the underlying distribution is univariate.

Author

Matthias Kohl Matthias.Kohl@stamats.de, Peter Ruckdeschel peter.ruckdeschel@uni-oldenburg.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.