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

Description Usage Arguments Value Methods Author(s) References See Also

Description

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

Usage

 1
 2
 3
 4
 5
 6
 7
 8
 9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
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 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.

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 [email protected], Peter Ruckdeschel [email protected]

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 May 31, 2017, 2:50 a.m.