getMaxIneff {ROptEst}

getMaxIneff – computation of the maximal inefficiency of an IC

Description

computes the maximal inefficiency of an IC for the radius range [0,Inf).

Usage

getMaxIneff(IC, neighbor, biastype = symmetricBias(), 
                        normtype = NormType(), z.start = NULL, 
                        A.start = NULL, maxiter = 50, 
                        tol = .Machine$double.eps^0.4,
                        warn = TRUE, verbose = NULL, ...)

Arguments

IC

some IC of class IC

neighbor

object of class Neighborhood; the neighborhood at which to compute the bias.

biastype

a bias type of class BiasType

normtype

a norm type of class NormType

z.start

initial value for the centering constant.

A.start

initial value for the standardizing matrix.

maxiter

the maximum number of iterations.

tol

the desired accuracy (convergence tolerance).

warn

logical: print warnings.

verbose

logical: if TRUE, some messages are printed

...

additional arguments to be passed to E

Value

The maximal inefficiency, i.e.; a number in [1,Inf).

Author(s)

Peter Ruckdeschel [e-mail]

References

Hampel et al. (1986) Robust Statistics. The Approach Based on Influence Functions. New York: Wiley.

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

Examples

N0 <- NormLocationFamily(mean=2, sd=3)
## L_2 family + infinitesimal neighborhood
neighbor <- ContNeighborhood(radius = 0.5)
N0.Rob1 <- InfRobModel(center = N0, neighbor = neighbor)
## OBRE solution (ARE 95%)
N0.ICA <- optIC(model = N0.Rob1, risk = asAnscombe(.95))
## OMSE solution radius 0.5
N0.ICM <- optIC(model=N0.Rob1, risk=asMSE())
## RMX solution 
N0.ICR <- radiusMinimaxIC(L2Fam=N0, neighbor=neighbor,risk=asMSE())

getMaxIneff(N0.ICA,neighbor)
getMaxIneff(N0.ICM,neighbor)
getMaxIneff(N0.ICR,neighbor)

## Don't run to reduce check time on CRAN

N0ls <- NormLocationScaleFamily()
ICsc <- makeIC(list(sin,cos),N0ls)
getMaxIneff(ICsc,neighbor)