getInfRad {ROptEst} | R Documentation |
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 signature
## 'numeric,UnivariateDistribution,asMSE,ContNeighborhood'
getInfRad(
clip, L2deriv, risk, neighbor, biastype, cent, symm, trafo)
## S4 method for signature
## 'numeric,UnivariateDistribution,asMSE,TotalVarNeighborhood'
getInfRad(
clip, L2deriv, risk, neighbor, biastype, cent, symm, trafo)
## S4 method for signature
## 'numeric,UnivariateDistribution,asL1,ContNeighborhood'
getInfRad(
clip, L2deriv, risk, neighbor, biastype, cent, symm, trafo)
## S4 method for signature
## 'numeric,UnivariateDistribution,asL1,TotalVarNeighborhood'
getInfRad(
clip, L2deriv, risk, neighbor, biastype, cent, symm, trafo)
## S4 method for signature
## 'numeric,UnivariateDistribution,asL4,ContNeighborhood'
getInfRad(
clip, L2deriv, risk, neighbor, biastype, cent, symm, trafo)
## S4 method for signature
## 'numeric,UnivariateDistribution,asL4,TotalVarNeighborhood'
getInfRad(
clip, L2deriv, risk, neighbor, biastype, cent, symm, trafo)
## S4 method for signature 'numeric,EuclRandVariable,asMSE,UncondNeighborhood'
getInfRad(
clip, L2deriv, risk, neighbor, biastype, Distr, stand, cent, trafo, ...)
## S4 method for signature
## 'numeric,UnivariateDistribution,asUnOvShoot,UncondNeighborhood'
getInfRad(
clip, L2deriv, risk, neighbor, biastype, cent, symm, trafo)
## S4 method for signature
## 'numeric,UnivariateDistribution,asSemivar,ContNeighborhood'
getInfRad(
clip, L2deriv, risk, neighbor, biastype, cent, symm, trafo)
Arguments
clip |
positive real: clipping bound |
L2deriv |
L2-derivative of some L2-differentiable family of probability measures. |
risk |
object of class |
neighbor |
object of class |
... |
additional parameters. |
biastype |
object of class |
cent |
optimal centering constant. |
stand |
standardizing matrix. |
Distr |
object of class |
symm |
logical: indicating symmetry of |
trafo |
matrix: transformation of the parameter. |
Value
The optimal clipping bound is computed.
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(s)
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.
See Also
ContIC-class
, TotalVarIC-class