cniperCont {ROptEst}R Documentation

Generic Functions for Computation and Plot of Cniper Contamination and Cniper Points.

Description

These generic functions and their methods can be used to determine cniper contamination as well as cniper points. That is, under which (Dirac) contamination is the risk of one procedure larger than the risk of some other procedure.

Usage

cniperCont(IC1, IC2, L2Fam, neighbor, risk, ...)
## S4 method for signature 'IC, IC, L2ParamFamily,
##   ContNeighborhood, asMSE':
cniperCont(IC1, 
      IC2, L2Fam, neighbor, risk, lower, upper, n = 101)

cniperPoint(L2Fam, neighbor, risk, ...)
## S4 method for signature 'L2ParamFamily,
##   ContNeighborhood, asMSE':
cniperPoint(L2Fam, 
      neighbor, risk, lower, upper)

cniperPointPlot(L2Fam, neighbor, risk, ...)
## S4 method for signature 'L2ParamFamily,
##   ContNeighborhood, asMSE':
cniperPointPlot(L2Fam, 
      neighbor, risk, lower, upper, n = 101)

Arguments

IC1 object of class IC
IC2 object of class IC
L2Fam object of class L2ParamFamily
neighbor object of class Neighborhood
risk object of class RiskType
... additional parameters.
lower, upper the lower and upper end points of the contamination interval.
n number of points between lower and upper

Details

In case of cniperCont the difference between the risks of two ICs is plotted.

The function cniperPoint can be used to determine cniper points. That is, points such that the optimally robust estimator has smaller minimax risk than the classical optimal estimator under contamination with Dirac measures at the cniper points.

As such points might be difficult to find, we provide the function cniperPointPlot which can be used to obtain a plot of the risk difference.

For more details about cniper contamination and cniper points we refer to Section~3.5 of Kohl et al. (2008) as well as Ruckdeschel (2004) and the Introduction of Kohl (2005).

Value

invisible() resp. cniper point is returned.

Author(s)

Matthias Kohl Matthias.Kohl@stamats.de

References

Kohl, M. and Ruckdeschel, H. and Rieder, H. (2008). Infinitesimally Robust Estimation in General Smoothly Parametrized Models. Unpublished Manuscript.

Kohl, M. (2005) Numerical Contributions to the Asymptotic Theory of Robustness. Bayreuth: Dissertation.

Ruckdeschel, P. (2004). Higher Order Asymptotics for the MSE of M-Estimators on Shrinking Neighborhoods. Unpublished Manuscript.

Examples

## cniper contamination
P <- PoisFamily(lambda = 4)
RobP1 <- InfRobModel(center = P, neighbor = ContNeighborhood(radius = 0.1))
IC1 <- optIC(model=RobP1, risk=asMSE())
RobP2 <- InfRobModel(center = P, neighbor = ContNeighborhood(radius = 1))
IC2 <- optIC(model=RobP2, risk=asMSE())
cniperCont(IC1 = IC1, IC2 = IC2, L2Fam = P, 
           neighbor = ContNeighborhood(radius = 0.5), 
           risk = asMSE(),
           lower = 0, upper = 8, n = 101)

## cniper point plot
cniperPointPlot(P, neighbor = ContNeighborhood(radius = 0.5), 
                risk = asMSE(), lower = 0, upper = 10)

## cniper point
cniperPoint(P, neighbor = ContNeighborhood(radius = 0.5), 
            risk = asMSE(), lower = 0, upper = 4)
cniperPoint(P, neighbor = ContNeighborhood(radius = 0.5), 
            risk = asMSE(), lower = 4, upper = 8)

[Package ROptEst version 0.6.3 Index]