getInfRobIC {ROptEst} | R Documentation |
Generic Function for the Computation of Optimally Robust ICs
Description
Generic function for the computation of optimally robust ICs in case of infinitesimal robust models. This function is rarely called directly.
Usage
getInfRobIC(L2deriv, risk, neighbor, ...)
## S4 method for signature 'UnivariateDistribution,asCov,ContNeighborhood'
getInfRobIC(L2deriv,
risk, neighbor, Finfo, trafo, verbose = NULL)
## S4 method for signature 'UnivariateDistribution,asCov,TotalVarNeighborhood'
getInfRobIC(L2deriv,
risk, neighbor, Finfo, trafo, verbose = NULL)
## S4 method for signature 'RealRandVariable,asCov,UncondNeighborhood'
getInfRobIC(L2deriv, risk,
neighbor, Distr, Finfo, trafo, QuadForm = diag(nrow(trafo)),
verbose = NULL)
## S4 method for signature 'UnivariateDistribution,asBias,UncondNeighborhood'
getInfRobIC(L2deriv,
risk, neighbor, symm, trafo, maxiter, tol, warn, Finfo,
verbose = NULL, ...)
## S4 method for signature 'RealRandVariable,asBias,UncondNeighborhood'
getInfRobIC(L2deriv, risk,
neighbor, Distr, DistrSymm, L2derivSymm,
L2derivDistrSymm, z.start, A.start, Finfo, trafo,
maxiter, tol, warn, verbose = NULL, ...)
## S4 method for signature 'UnivariateDistribution,asHampel,UncondNeighborhood'
getInfRobIC(L2deriv,
risk, neighbor, symm, Finfo, trafo, upper = NULL,
lower=NULL, maxiter, tol, warn, noLow = FALSE,
verbose = NULL, checkBounds = TRUE, ...)
## S4 method for signature 'RealRandVariable,asHampel,UncondNeighborhood'
getInfRobIC(L2deriv, risk,
neighbor, Distr, DistrSymm, L2derivSymm,
L2derivDistrSymm, Finfo, trafo, onesetLM = FALSE,
z.start, A.start, upper = NULL, lower=NULL,
OptOrIter = "iterate", maxiter, tol, warn,
verbose = NULL, checkBounds = TRUE, ...,
.withEvalAsVar = TRUE)
## S4 method for signature
## 'UnivariateDistribution,asAnscombe,UncondNeighborhood'
getInfRobIC(
L2deriv, risk, neighbor, symm, Finfo, trafo, upper = NULL,
lower=NULL, maxiter, tol, warn, noLow = FALSE,
verbose = NULL, checkBounds = TRUE, ...)
## S4 method for signature 'RealRandVariable,asAnscombe,UncondNeighborhood'
getInfRobIC(L2deriv,
risk, neighbor, Distr, DistrSymm, L2derivSymm,
L2derivDistrSymm, Finfo, trafo, onesetLM = FALSE,
z.start, A.start, upper = NULL, lower=NULL,
OptOrIter = "iterate", maxiter, tol, warn,
verbose = NULL, checkBounds = TRUE, ...)
## S4 method for signature 'UnivariateDistribution,asGRisk,UncondNeighborhood'
getInfRobIC(L2deriv,
risk, neighbor, symm, Finfo, trafo, upper = NULL,
lower = NULL, maxiter, tol, warn, noLow = FALSE,
verbose = NULL, ...)
## S4 method for signature 'RealRandVariable,asGRisk,UncondNeighborhood'
getInfRobIC(L2deriv, risk,
neighbor, Distr, DistrSymm, L2derivSymm,
L2derivDistrSymm, Finfo, trafo, onesetLM = FALSE, z.start,
A.start, upper = NULL, lower = NULL, OptOrIter = "iterate",
maxiter, tol, warn, verbose = NULL, withPICcheck = TRUE,
..., .withEvalAsVar = TRUE)
## S4 method for signature
## 'UnivariateDistribution,asUnOvShoot,UncondNeighborhood'
getInfRobIC(
L2deriv, risk, neighbor, symm, Finfo, trafo,
upper, lower, maxiter, tol, warn, verbose = NULL, ...)
Arguments
L2deriv |
L2-derivative of some L2-differentiable family of probability measures. |
risk |
object of class |
neighbor |
object of class |
... |
additional parameters (mainly for |
Distr |
object of class |
symm |
logical: indicating symmetry of |
DistrSymm |
object of class |
L2derivSymm |
object of class |
L2derivDistrSymm |
object of class |
Finfo |
Fisher information matrix. |
z.start |
initial value for the centering constant. |
A.start |
initial value for the standardizing matrix. |
trafo |
matrix: transformation of the parameter. |
upper |
upper bound for the optimal clipping bound. |
lower |
lower bound for the optimal clipping bound. |
OptOrIter |
character; which method to be used for determining Lagrange
multipliers |
maxiter |
the maximum number of iterations. |
tol |
the desired accuracy (convergence tolerance). |
warn |
logical: print warnings. |
noLow |
logical: is lower case to be computed? |
onesetLM |
logical: use one set of Lagrange multipliers? |
QuadForm |
matrix of (or which may coerced to) class
|
verbose |
logical: if |
checkBounds |
logical: if |
withPICcheck |
logical: at the end of the algorithm, shall we check
how accurately this is a pIC; this will only be done if
|
.withEvalAsVar |
logical (of length 1):
if |
Value
The optimally robust IC is computed.
Methods
- L2deriv = "UnivariateDistribution", risk = "asCov", neighbor = "ContNeighborhood"
-
computes the classical optimal influence curve for L2 differentiable parametric families with unknown one-dimensional parameter.
- L2deriv = "UnivariateDistribution", risk = "asCov", neighbor = "TotalVarNeighborhood"
-
computes the classical optimal influence curve for L2 differentiable parametric families with unknown one-dimensional parameter.
- L2deriv = "RealRandVariable", risk = "asCov", neighbor = "UncondNeighborhood"
-
computes the classical optimal influence curve for L2 differentiable parametric families with unknown
k
-dimensional parameter (k > 1
) where the underlying distribution is univariate; for total variation neighborhoods only is implemented for the case where there is a1\times k
transformationtrafo
matrix. - L2deriv = "UnivariateDistribution", risk = "asBias", neighbor = "UncondNeighborhood"
-
computes the bias optimal influence curve for L2 differentiable parametric families with unknown one-dimensional parameter.
- L2deriv = "RealRandVariable", risk = "asBias", neighbor = "UncondNeighborhood"
-
computes the bias optimal influence curve for L2 differentiable parametric families with unknown
k
-dimensional parameter (k > 1
) where the underlying distribution is univariate. - L2deriv = "UnivariateDistribution", risk = "asHampel", neighbor = "UncondNeighborhood"
-
computes the optimally robust influence curve for L2 differentiable parametric families with unknown one-dimensional parameter.
- L2deriv = "RealRandVariable", risk = "asHampel", neighbor = "UncondNeighborhood"
-
computes the optimally robust influence curve for L2 differentiable parametric families with unknown
k
-dimensional parameter (k > 1
) where the underlying distribution is univariate; for total variation neighborhoods only is implemented for the case where there is a1\times k
transformationtrafo
matrix. - L2deriv = "UnivariateDistribution", risk = "asAnscombe", neighbor = "UncondNeighborhood"
-
computes the optimally bias-robust influence curve to given ARE in the ideal model for L2 differentiable parametric families with unknown one-dimensional parameter.
- L2deriv = "RealRandVariable", risk = "asAnscombe", neighbor = "UncondNeighborhood"
-
computes the optimally bias-robust influence curve to given ARE in the ideal modelfor L2 differentiable parametric families with unknown
k
-dimensional parameter (k > 1
) where the underlying distribution is univariate; for total variation neighborhoods only is implemented for the case where there is a1\times k
transformationtrafo
matrix. - L2deriv = "UnivariateDistribution", risk = "asGRisk", neighbor = "UncondNeighborhood"
-
computes the optimally robust influence curve for L2 differentiable parametric families with unknown one-dimensional parameter.
- L2deriv = "RealRandVariable", risk = "asGRisk", neighbor = "UncondNeighborhood"
-
computes the optimally robust influence curve for L2 differentiable parametric families with unknown
k
-dimensional parameter (k > 1
) where the underlying distribution is univariate; for total variation neighborhoods only is implemented for the case where there is a1\times k
transformationtrafo
matrix. - L2deriv = "UnivariateDistribution", risk = "asUnOvShoot", neighbor = "UncondNeighborhood"
-
computes the optimally robust influence curve for one-dimensional L2 differentiable parametric families and asymptotic under-/overshoot risk.
Author(s)
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. 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.