cniperCont {ROptEst} | R Documentation |
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.
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)
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 |
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).
invisible() resp. cniper point is returned.
Matthias Kohl Matthias.Kohl@stamats.de
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 Unpublished Manuscript.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 Unpublished Manuscript.
## 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)