optIC: Generic function for the computation of optimally robust ICs

In ROptEstOld: Optimally Robust Estimation - Old Version

Description

Generic function for the computation of optimally robust ICs.

Usage

optIC(model, risk, ...)

## S4 method for signature 'L2ParamFamily,asCov'
optIC(model, risk)

## S4 method for signature '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 signature 'InfRobModel,asUnOvShoot'
optIC(model, risk, upper = 1e4, maxiter = 50, 
             tol = .Machine$double.eps^0.4, warn = TRUE)

## S4 method for signature '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".

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).

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.

Author(s)

Matthias Kohl [e-mail]

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

B <- BinomFamily(size = 25, prob = 0.25) 

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

ROptEstOld documentation built on May 2, 2019, 12:51 p.m.