rgsOptIC.M {RobRex}R Documentation

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.

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.

Value

Object of class "IC"

Author(s)

Matthias Kohl Matthias.Kohl@stamats.de

References

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

See Also

IC-class

Examples

## 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)
## End(Not run)

[Package RobRex version 0.6.1 Index]