optIC-methods: Methods for Function optIC in Package `ROptRegTS'

Description

Methods for function optIC in package ROptRegTS.

Usage

# S4 method for L2RegTypeFamily,asCov
optIC(model, risk)
# S4 method for InfRobRegTypeModel,asRisk
optIC(model, risk, z.start = NULL,
                 A.start = NULL, upper = 1e4, maxiter = 50,
                 tol = .Machine$double.eps^0.4, warn = TRUE)
# S4 method for InfRobRegTypeModel,asUnOvShoot
optIC(model, risk, upper = 1e4,
                 maxiter = 50, tol = .Machine$double.eps^0.4, warn = TRUE)
# S4 method for FixRobRegTypeModel,fiUnOvShoot
optIC(model, risk, sampleSize,
                 upper = 1e4, maxiter = 50, tol = .Machine$double.eps^0.4,
                 warn = TRUE, Algo = "A", cont = "left")

Arguments

model

probability model.

risk

object of class "RiskType".

z.start

initial value for the centering constant.

A.start

initial value for the standardizing matrix.

upper

upper bound for the optimal clipping bound.

maxiter

the maximum number of iterations.

tol

the desired accuracy (convergence tolerance).

warn

logical: print warnings.

sampleSize

integer: sample size.

Algo

"A" or "B".

cont

"left" or "right".

Value

Some optimally robust IC is computed.

Methods

model = "L2RegTypeFamily", risk = "asCov": computes classical optimal influence curve for L2 differentiable regression-type families.
model = "InfRobRegTypeModel", risk = "asRisk": computes optimally robust influence curve for robust regression-type models with infinitesimal neighborhoods and various asymptotic risks.
model = "InfRobRegTypeModel", risk = "asUnOvShoot": computes optimally robust influence curve for robust regression-type models with infinitesimal neighborhoods and asymptotic under-/overshoot risk.
model = "FixRobRegTypeModel", risk = "fiUnOvShoot": computes optimally robust influence curve for robust regression-type models with fixed neighborhoods and finite-sample under-/overshoot risk.

Details

In case of the finite-sample risk "fiUnOvShoot" one can choose between two algorithms for the computation of this risk where the least favorable contamination is assumed to be “left” or “right” of some boundary curve. For more details we refer to Subsections 12.1.3 and 12.2.3 of Kohl (2005).

References

Huber, P.J. (1968) Robust Confidence Limits. Z. Wahrscheinlichkeitstheor. Verw. Geb. 10:269--278.

Rieder, H. (1980) Estimates derived from robust tests. Ann. Stats. 8: 106--115.

Rieder, H. (1994) Robust Asymptotic Statistics. New York: Springer.

Kohl, M. (2005) Numerical Contributions to the Asymptotic Theory of Robustness. Bayreuth: Dissertation.