rgsOptIC.M: Computation of the optimally robust IC for M estimators
In RobRex: Optimally Robust Influence Curves for Regression and Scale

Description Usage Arguments Details Value Author(s) References See Also Examples

View source: R/rgsOptIC_M.R

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).

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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)

`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.

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.

Object of class "IC"

Matthias Kohl Matthias.Kohl@stamats.de

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

IC-class

## 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)