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

Description

The function rgsOptIC.Mc computes the optimally robust conditionally centered IC for Mc estimators in case of linear regression with unknown scale and average conditional (convex) contamination neighborhoods where the regressor is random; confer Subsubsection 7.2.2.2 of Kohl (2005).

Usage

rgsOptIC.Mc(r, K, ggLo = 0.5, ggUp = 1, a1.x.start, a3.start = 0.25, 
             bUp = 1000, delta = 1e-05, itmax = 1000, check = FALSE)

Arguments

non-negative real: neighborhood radius.

object of class "DiscreteDistribution"

ggLo

positive real: the lower end point of the interval to be searched for \(\gamma\).

ggUp

positive real: the upper end point of the interval to be searched for \(\gamma\).

a1.x.start

real: starting value for the Lagrange multiplier function \(\alpha_1(x)\).

a3.start

real: starting value for Lagrange multiplier \(\alpha_3\).

bUp

positive real: the upper end point of the interval to be searched for b.

delta

the desired accuracy (convergence tolerance).

itmax

the maximum number of iterations.

check

logical. Should constraints be checked.

Value

Object of class "CondIC"

References

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

Examples

Run this code

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