getInfRad: Generic Function for the Computation of the Optimal Radius for Given Clipping Bound

Description

The usual robust optimality problem for given asGRisk searches the optimal clipping height b of a Hampel-type IC to given radius of the neighborhood. Instead, again for given asGRisk and for given Hampel-Type IC with given clipping height b we may determine the radius of the neighborhood for which it is optimal in the sense of the first sentence. This radius is determined by getInfRad. This function is rarely called directly. It is used withing getRadius.

Usage

getInfRad(clip, L2deriv, risk, neighbor, ...)
# S4 method for numeric,UnivariateDistribution,asMSE,ContNeighborhood
getInfRad(
          clip, L2deriv, risk, neighbor, biastype, cent, symm, trafo)
# S4 method for numeric,UnivariateDistribution,asMSE,TotalVarNeighborhood
getInfRad(
          clip, L2deriv, risk, neighbor, biastype, cent, symm, trafo)
# S4 method for numeric,UnivariateDistribution,asL1,ContNeighborhood
getInfRad(
          clip, L2deriv, risk, neighbor, biastype, cent, symm, trafo)
# S4 method for numeric,UnivariateDistribution,asL1,TotalVarNeighborhood
getInfRad(
          clip, L2deriv, risk, neighbor, biastype, cent, symm, trafo)
# S4 method for numeric,UnivariateDistribution,asL4,ContNeighborhood
getInfRad(
          clip, L2deriv, risk, neighbor, biastype, cent, symm, trafo)
# S4 method for numeric,UnivariateDistribution,asL4,TotalVarNeighborhood
getInfRad(
          clip, L2deriv, risk, neighbor, biastype, cent, symm, trafo)
# S4 method for numeric,EuclRandVariable,asMSE,UncondNeighborhood
getInfRad(
          clip, L2deriv, risk, neighbor, biastype, Distr, stand, cent, trafo, ...)
# S4 method for numeric,UnivariateDistribution,asUnOvShoot,UncondNeighborhood
getInfRad(
          clip, L2deriv, risk, neighbor, biastype, cent, symm, trafo)
# S4 method for numeric,UnivariateDistribution,asSemivar,ContNeighborhood
getInfRad(
          clip, L2deriv, risk, neighbor, biastype, cent, symm, trafo)

Value

The optimal clipping bound is computed.

Arguments

clip: positive real: clipping bound
L2deriv: L2-derivative of some L2-differentiable family of probability measures.
risk: object of class "RiskType".
neighbor: object of class "Neighborhood".
...: additional parameters.
biastype: object of class "BiasType"
cent: optimal centering constant.
stand: standardizing matrix.
Distr: object of class "Distribution".
symm: logical: indicating symmetry of L2deriv.
trafo: matrix: transformation of the parameter.

Methods

clip = "numeric", L2deriv = "UnivariateDistribution", risk = "asMSE", neighbor = "ContNeighborhood": optimal clipping bound for asymtotic mean square error.
clip = "numeric", L2deriv = "UnivariateDistribution", risk = "asMSE", neighbor = "TotalVarNeighborhood": optimal clipping bound for asymtotic mean square error.
clip = "numeric", L2deriv = "EuclRandVariable", risk = "asMSE", neighbor = "UncondNeighborhood": optimal clipping bound for asymtotic mean square error.
clip = "numeric", L2deriv = "UnivariateDistribution", risk = "asL1", neighbor = "ContNeighborhood": optimal clipping bound for asymtotic mean absolute error.
clip = "numeric", L2deriv = "UnivariateDistribution", risk = "asL1", neighbor = "TotalVarNeighborhood": optimal clipping bound for asymtotic mean absolute error.
clip = "numeric", L2deriv = "UnivariateDistribution", risk = "asL4", neighbor = "ContNeighborhood": optimal clipping bound for asymtotic mean power 4 error.
clip = "numeric", L2deriv = "UnivariateDistribution", risk = "asL4", neighbor = "TotalVarNeighborhood": optimal clipping bound for asymtotic mean power 4 error.
clip = "numeric", L2deriv = "UnivariateDistribution", risk = "asUnOvShoot", neighbor = "UncondNeighborhood": optimal clipping bound for asymtotic under-/overshoot risk.
clip = "numeric", L2deriv = "UnivariateDistribution", risk = "asSemivar", neighbor = "ContNeighborhood": optimal clipping bound for asymtotic semivariance.

Author

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. and Rieder, H. (2004) Optimal Influence Curves for General Loss Functions. Statistics & Decisions 22, 201-223.

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.