minmaxBias: Generic Function for the Computation of Bias-Optimally Robust...

In ROptEst: Optimally Robust Estimation

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, verbose = NULL)

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

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

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

## S4 method for signature '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 signature 'RealRandVariable,TotalVarNeighborhood,BiasType'
minmaxBias(L2deriv,
     neighbor, biastype, normtype, Distr, z.start, A.start,  z.comp, A.comp,
     Finfo, trafo, maxiter, tol, verbose = NULL, ...)

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

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.

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(s)

Matthias Kohl [e-mail], Peter Ruckdeschel [e-mail]

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

ROptEst documentation built on Nov. 17, 2022, 1:06 a.m.