radiusMinimaxIC | R Documentation |
Generic function for the computation of the radius minimax IC.
radiusMinimaxIC(L2Fam, neighbor, risk, ...)
## S4 method for signature 'L2ParamFamily,UncondNeighborhood,asGRisk'
radiusMinimaxIC(
L2Fam, neighbor, risk, loRad = 0, upRad = Inf, z.start = NULL, A.start = NULL,
upper = NULL, lower = NULL, OptOrIter = "iterate",
maxiter = 50, tol = .Machine$double.eps^0.4,
warn = FALSE, verbose = NULL, loRad0 = 1e-3, ...,
returnNAifProblem = FALSE, loRad.s = NULL, upRad.s = NULL,
modifyICwarn = NULL)
L2Fam |
L2-differentiable family of probability measures. |
neighbor |
object of class |
risk |
object of class |
loRad |
the lower end point of the interval to be searched in the inner optimization (for the least favorable situation to the user-guessed radius). |
upRad |
the upper end point of the interval to be searched in the inner optimization (for the least favorable situation to the user-guessed radius). |
z.start |
initial value for the centering constant. |
A.start |
initial value for the standardizing matrix. |
upper |
upper bound for the optimal clipping bound. |
lower |
lower bound for the optimal clipping bound. |
OptOrIter |
character; which method to be used for determining Lagrange
multipliers |
maxiter |
the maximum number of iterations |
tol |
the desired accuracy (convergence tolerance). |
warn |
logical: print warnings. |
verbose |
logical: if |
loRad0 |
for numerical reasons: the effective lower bound for the zero search;
internally set to |
... |
further arguments to be passed on to |
returnNAifProblem |
logical (of length 1):
if |
loRad.s |
the lower end point of the interval
to be searched in the outer optimization
(for the user-guessed radius); if |
upRad.s |
the upper end point of the interval to be searched in the
outer optimization (for the user-guessed radius); if
|
modifyICwarn |
logical: should a (warning) information be added if
|
In case the neighborhood radius is unknown, Rieder et al. (2001, 2008) and Kohl (2005) show that there is nevertheless a way to compute an optimally robust IC - the so-called radius-minimax IC - which is optimal for some radius interval.
The radius minimax IC is computed.
computation of the radius minimax IC for an L2 differentiable parametric family.
Matthias Kohl Matthias.Kohl@stamats.de, Peter Ruckdeschel peter.ruckdeschel@uni-oldenburg.de
M. Kohl (2005). Numerical Contributions to the Asymptotic Theory of Robustness. Bayreuth: Dissertation. https://epub.uni-bayreuth.de/id/eprint/839/2/DissMKohl.pdf.
H. Rieder, M. Kohl, and P. Ruckdeschel (2008). The Costs of not Knowing the Radius. Statistical Methods and Applications, 17(1) 13-40. \Sexpr[results=rd]{tools:::Rd_expr_doi("10.1007/s10260-007-0047-7")}.
H. Rieder, M. Kohl, and P. Ruckdeschel (2001). The Costs of not Knowing the Radius. Appeared as discussion paper Nr. 81. SFB 373 (Quantification and Simulation of Economic Processes), Humboldt University, Berlin; also available under \Sexpr[results=rd]{tools:::Rd_expr_doi("10.18452/3638")}.
P. Ruckdeschel (2005). Optimally One-Sided Bounded Influence Curves. Mathematical Methods of Statistics 14(1), 105-131.
P. Ruckdeschel and H. Rieder (2004). Optimal Influence Curves for General Loss Functions. Statistics & Decisions 22, 201-223. \Sexpr[results=rd]{tools:::Rd_expr_doi("10.1524/stnd.22.3.201.57067")}
radiusMinimaxIC
N <- NormLocationFamily(mean=0, sd=1)
radIC <- radiusMinimaxIC(L2Fam=N, neighbor=ContNeighborhood(),
risk=asMSE(), loRad=0.1, upRad=0.5)
checkIC(radIC)
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