rgsOptIC.BM: Computation of the optimally robust IC for BM estimators

In RobRex: Optimally Robust Influence Curves for Regression and Scale

Computation of the optimally robust IC for BM estimators

Description

The function rgsOptIC.BM computes the optimally robust IC for BM estimators in case of linear regression with unknown scale and (convex) contamination neighborhoods where the regressor is random. These estimators were proposed by Bednarski and Mueller (2001); confer also Subsection 7.3.3 of Kohl (2005).

Usage

rgsOptIC.BM(r, K, b.rg.start = 2.5, b.sc.0.x.start, delta = 1e-06, 
            MAX = 100, itmax = 1000)

Arguments

r	non-negative real: neighborhood radius.
K	object of class "DiscreteDistribution"
b.rg.start	positive real: starting value for b_{\rm rg}.
b.sc.0.x.start	positive real: starting value for b_{{\rm sc},0,x}.
delta	the desired accuracy (convergence tolerance).
itmax	the maximum number of iterations.
MAX	if b_{\rm loc} or b_{{\rm sc},0} are beyond the admitted values, MAX is returned.

Details

The computation of the optimally robust IC for BM estimators is based on optim where MAX is used to control the constraints on b_{\rm rg} and b_{{\rm sc},0,x}.

Value

Object of class "CondIC"

Author(s)

Matthias Kohl [e-mail]

References

Bednarski, T and Mueller, C.H. (2001) Optimal bounded influence regression and scale M-estimators in the context of experimental design. Statistics, 35(4): 349–369.

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

See Also

CondIC-class

Examples

## code takes some time
## Not run: 
K <- DiscreteDistribution(1:5) # = Unif({1,2,3,4,5})
IC1 <- rgsOptIC.BM(r = 0.1, K = K)
checkIC(IC1)
Risks(IC1)

## End(Not run)

RobRex documentation built on Jan. 29, 2024, 3:01 a.m.