Computation of the optimally robust IC for BM estimators
The function rlsOptIC.BM computes the optimally robust IC for
BM estimators in case of normal location with unknown scale and
(convex) contamination neighborhoods. These estimators were proposed
by Bednarski and Mueller (2001). A definition of these
estimators can also be found in Section 8.4 of Kohl (2005).
rlsOptIC.BM(r, bL.start = 2, bS.start = 1.5, delta = 1e-06, MAX = 100)
r |
non-negative real: neighborhood radius. |
bL.start |
positive real: starting value for b_loc. |
bS.start |
positive real: starting value for b_sc,0. |
delta |
the desired accuracy (convergence tolerance). |
MAX |
if b_loc or b_sc,0
are beyond the admitted values, |
The computation of the optimally robust IC for BM estimators
is based on optim where MAX is used to
control the constraints on b_loc
and b_sc,0. The optimal values of the
tuning constants b_loc, b_sc,0,
alpha and gamma can be read off
from the slot Infos of the resulting IC.
Object of class "IC"
Matthias Kohl Matthias.Kohl@stamats.de
Bednarski, T and Mueller, C.H. (2001) Optimal bounded influence regression and scale M-estimators in the context of experimental design. Statistics, 35(4): 349–369.
Kohl, M. (2005) Numerical Contributions to the Asymptotic Theory of Robustness. Bayreuth: Dissertation.
IC1 <- rlsOptIC.BM(r = 0.1) checkIC(IC1) Risks(IC1) Infos(IC1) plot(IC1) infoPlot(IC1)
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