RobRex (version 1.2.0)

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

Description

The function rgsOptIC.M computes the optimally robust IC for M estimators in case of linear regression with unknown scale and (convex) contamination neighborhoods where the regressor is random; confer Subsubsection 7.2.2.1 of Kohl (2005).

Usage

rgsOptIC.M(r, K, A.start, gg.start = 0.6, a1.start = -0.25, 
            a3.start = 0.25, B.start, bUp = 1000, delta = 1e-05, 
            MAX = 100, itmax = 1000, check = FALSE)

Arguments

r

non-negative real: neighborhood radius.

K

object of class "Distribution".

A.start

positive definite and symmetric matrix: starting value for the standardizing matrix of the regression part.

gg.start

positive real: starting value for the standardizing constant \(\gamma\) of the scale part.

a1.start

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

a3.start

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

B.start

symmetric matrix: starting value for Lagrange multiplier B.

bUp

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

delta

the desired accuracy (convergence tolerance).

MAX

if A or \(\gamma\) are beyond the admitted values, MAX is returned.

itmax

the maximum number of iterations.

check

logical. Should constraints be checked.

Value

Object of class "IC"

Details

The computation of the optimally robust IC for M estimators is based on optim where MAX is used to control the constraints on A and \(\gamma\).

References

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

See Also

IC-class

Examples

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