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

In RobRex: Optimally Robust Influence Curves for Regression and Scale

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 [e-mail]

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)

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