getIneffDiff {ROptEst}

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. 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 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. doi:10.1524/stnd.22.3.201.57067

See Also

radiusMinimaxIC, leastFavorableRadius