getIneffDiff: Generic Function for the Computation of Inefficiency...

In ROptEst: Optimally Robust Estimation

Generic Function for the Computation of Inefficiency Differences

Description

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.

Usage

getIneffDiff(radius, L2Fam, neighbor, risk, ...)

## S4 method for signature '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)

Arguments

radius	neighborhood radius.
L2Fam	L2-differentiable family of probability measures.
neighbor	object of class "Neighborhood".
risk	object of class "RiskType".
loRad	the lower end point of the interval to be searched.
upRad	the upper end point of the interval to be searched.
loRisk	the risk at the lower end point of the interval.
upRisk	the risk at the upper end point of the interval.
z.start	initial value for the centering constant.
A.start	initial value for the standardizing matrix.
upper.b	upper bound for the optimal clipping bound.
lower.b	lower bound for the optimal clipping bound.
OptOrIter	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.
MaxIter	the maximum number of iterations
eps	the desired accuracy (convergence tolerance).
warn	logical: print warnings.
loNorm	object of class "NormType"; used in selfstandardization to evaluate the bias of the current IC in the norm of the lower bound
upNorm	object of class "NormType"; used in selfstandardization to evaluate the bias of the current IC in the norm of the upper bound
verbose	logical: if TRUE, some messages are printed
...	further arguments to be passed on to getInfRobIC
withRetIneff	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.

Value

The inefficieny difference between the left and the right margin of a given radius interval is computed.

Methods

radius = "numeric", L2Fam = "L2ParamFamily", neighbor = "UncondNeighborhood", risk = "asMSE":

computes difference of asymptotic MSE–inefficiency for the boundaries of a given radius interval.

Author(s)

Matthias Kohl [e-mail]

References

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")}

See Also

radiusMinimaxIC, leastFavorableRadius

ROptEst documentation built on Sept. 12, 2024, 7:40 a.m.