ROptEstOld (version 1.2.0)

optIC: Generic function for the computation of optimally robust ICs

Description

Generic function for the computation of optimally robust ICs.

Usage

optIC(model, risk, ...)
# S4 method for L2ParamFamily,asCov
optIC(model, risk)
# S4 method for InfRobModel,asRisk
optIC(model, risk, z.start = NULL, A.start = NULL, upper = 1e4, 
             maxiter = 50, tol = .Machine$double.eps^0.4, warn = TRUE)
# S4 method for InfRobModel,asUnOvShoot
optIC(model, risk, upper = 1e4, maxiter = 50, 
             tol = .Machine$double.eps^0.4, warn = TRUE)
# S4 method for FixRobModel,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".

…

additional parameters.

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 = "L2ParamFamily", risk = "asCov"

computes classical optimal influence curve for L2 differentiable parametric families.

model = "InfRobModel", risk = "asRisk"

computes optimally robust influence curve for robust models with infinitesimal neighborhoods and various asymptotic risks.

model = "InfRobModel", risk = "asUnOvShoot"

computes optimally robust influence curve for robust models with infinitesimal neighborhoods and asymptotic under-/overshoot risk.

model = "FixRobModel", risk = "fiUnOvShoot"

computes optimally robust influence curve for robust 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 bound. For more details we refer to Section 11.3 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.

See Also

InfluenceCurve-class, RiskType-class

Examples

# NOT RUN {
B <- BinomFamily(size = 25, prob = 0.25) 

## classical optimal IC
IC0 <- optIC(model = B, risk = asCov())
plot(IC0) # plot IC
checkIC(IC0, B)
# }