Computation of the optimally robust IC for HuMad estimators
The function rlsOptIC.HuMad computes the optimally robust IC for
HuMad estimators in case of normal location with unknown scale and
(convex) contamination neighborhoods. These estimators were
considered in Andrews et al. (1972). A definition of these estimators
can also be found in Subsection 8.5.2 of Kohl (2005).
rlsOptIC.HaMad(r, a.start = 0.25, b.start = 2.5, c.start = 5,
delta = 1e-06, MAX = 100)r |
non-negative real: neighborhood radius. |
a.start |
positive real: starting value for a. |
b.start |
positive real: starting value for b. |
c.start |
positive real: starting value for c. |
delta |
the desired accuracy (convergence tolerance). |
MAX |
if a or b or c are beyond the admitted values,
|
The computation of the optimally robust IC for HaMad estimators
is based on optim where MAX is used to
control the constraints on a, b and c. The optimal values of
the tuning constants a, b, and c can be read off
from the slot Infos of the resulting IC.
Object of class "IC"
Matthias Kohl Matthias.Kohl@stamats.de
Andrews, D.F., Bickel, P.J., Hampel, F.R., Huber, P.J., Rogers, W.H. and Tukey, J.W. (1972) Robust estimates of location. Princeton University Press.
Kohl, M. (2005) Numerical Contributions to the Asymptotic Theory of Robustness. Bayreuth: Dissertation.
IC1 <- rlsOptIC.HaMad(r = 0.1) checkIC(IC1) Risks(IC1) Infos(IC1) plot(IC1) infoPlot(IC1)
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