RobRex (version 1.2.0)

rgsOptIC.BM: 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.

Value

Object of class "CondIC"

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 \(b_{{\rm sc},0,x}\).

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

# NOT RUN {
## 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)
# }