Generic function for the computation of inefficiency differencies. This function is rarely called directly. It is used to compute the radius minimax IC and the least favorable radius.
getIneffDiff(radius, L2Fam, neighbor, risk, ...)# S4 method for numeric,L2ParamFamily,UncondNeighborhood,asMSE
getIneffDiff(
radius, L2Fam, neighbor, risk, loRad, upRad, loRisk, upRisk,
z.start = NULL, A.start = NULL, upper.b = NULL, lower.b = NULL,
OptOrIter = "iterate", MaxIter, eps, warn, loNorm = NULL, upNorm = NULL,
verbose = NULL, ..., withRetIneff = FALSE)
The inefficieny difference between the left and the right margin of a given radius interval is computed.
neighborhood radius.
L2-differentiable family of probability measures.
object of class "Neighborhood".
object of class "RiskType".
the lower end point of the interval to be searched.
the upper end point of the interval to be searched.
the risk at the lower end point of the interval.
the risk at the upper end point of the interval.
initial value for the centering constant.
initial value for the standardizing matrix.
upper bound for the optimal clipping bound.
lower bound for the optimal clipping bound.
character; which method to be used for determining Lagrange
multipliers A and a: if (partially) matched to "optimize",
getLagrangeMultByOptim is used; otherwise: by default, or if matched to
"iterate" or to "doubleiterate",
getLagrangeMultByIter is used. More specifically,
when using getLagrangeMultByIter, and if argument risk is of
class "asGRisk", by default and if matched to "iterate"
we use only one (inner) iteration, if matched to "doubleiterate"
we use up to Maxiter (inner) iterations.
the maximum number of iterations
the desired accuracy (convergence tolerance).
logical: print warnings.
object of class "NormType"; used in selfstandardization
to evaluate the bias of the current IC in the norm of the lower
bound
object of class "NormType"; used in selfstandardization
to evaluate the bias of the current IC in the norm of the upper
bound
logical: if TRUE, some messages are printed
further arguments to be passed on to getInfRobIC
logical: if TRUE, getIneffDiff returns the
vector of lower and upper inefficiency (components named "lo" and "up"),
otherwise (default) the difference.
The latter was used in radiusMinimaxIC up to version 0.8
for a call to uniroot directly. In order to speed up things
(i.e., not to call the expensive getInfRobIC once again at the zero,
up to version 0.8 we had some awkward assign-sys.frame
construction to modify the caller writing the upper inefficiency already
computed to the caller environment; having capsulated this into try
from version 0.9 on, this became even more awkward, so from version 0.9
onwards, we instead use the TRUE-alternative when calling it
from radiusMinimaxIC.
computes difference of asymptotic MSE--inefficiency for the boundaries of a given radius interval.
Matthias Kohl Matthias.Kohl@stamats.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. 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 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. tools:::Rd_expr_doi("10.1524/stnd.22.3.201.57067")
radiusMinimaxIC, leastFavorableRadius