getRiskIC: Generic function for the computation of a risk for an IC

Description

Generic function for the computation of a risk for an IC.

Usage

getRiskIC(IC, risk, neighbor, L2Fam, ...)
# S4 method for IC,asCov,missing,missing
getRiskIC(IC, risk, tol = .Machine$double.eps^0.25)
# S4 method for IC,asCov,missing,L2ParamFamily
getRiskIC(IC, risk, L2Fam, tol = .Machine$double.eps^0.25)
# S4 method for IC,trAsCov,missing,missing
getRiskIC(IC, risk, tol = .Machine$double.eps^0.25)
# S4 method for IC,trAsCov,missing,L2ParamFamily
getRiskIC(IC, risk, L2Fam, tol = .Machine$double.eps^0.25)
# S4 method for IC,asBias,ContNeighborhood,missing
getRiskIC(IC, risk, neighbor, tol = .Machine$double.eps^0.25)
# S4 method for IC,asBias,ContNeighborhood,L2ParamFamily
getRiskIC(IC, risk, neighbor, L2Fam, tol = .Machine$double.eps^0.25)
# S4 method for IC,asBias,TotalVarNeighborhood,missing
getRiskIC(IC, risk, neighbor, tol = .Machine$double.eps^0.25)
# S4 method for IC,asBias,TotalVarNeighborhood,L2ParamFamily
getRiskIC(IC, risk, neighbor, L2Fam, tol = .Machine$double.eps^0.25)
# S4 method for IC,asMSE,UncondNeighborhood,missing
getRiskIC(IC, risk, neighbor, tol = .Machine$double.eps^0.25)
# S4 method for IC,asMSE,UncondNeighborhood,L2ParamFamily
getRiskIC(IC, risk, neighbor, L2Fam, tol = .Machine$double.eps^0.25)
# S4 method for TotalVarIC,asUnOvShoot,UncondNeighborhood,missing
getRiskIC(IC, risk, neighbor)
# S4 method for IC,fiUnOvShoot,ContNeighborhood,missing
getRiskIC(IC, risk, neighbor, sampleSize, Algo = "A", cont = "left")
# S4 method for IC,fiUnOvShoot,TotalVarNeighborhood,missing
getRiskIC(IC, risk, neighbor, sampleSize, Algo = "A", cont = "left")

Arguments

object of class "InfluenceCurve"

risk

object of class "RiskType".

neighbor

object of class "Neighborhood".

L2Fam

object of class "L2ParamFamily".

…

additional parameters

tol

the desired accuracy (convergence tolerance).

sampleSize

integer: sample size.

Algo

"A" or "B".

cont

"left" or "right".

Value

The risk of an IC is computed.

Methods

IC = "IC", risk = "asCov", neighbor = "missing", L2Fam = "missing": asymptotic covariance of IC.
IC = "IC", risk = "asCov", neighbor = "missing", L2Fam = "L2ParamFamily": asymptotic covariance of IC under L2Fam.
IC = "IC", risk = "trAsCov", neighbor = "missing", L2Fam = "missing": asymptotic covariance of IC.
IC = "IC", risk = "trAsCov", neighbor = "missing", L2Fam = "L2ParamFamily": asymptotic covariance of IC under L2Fam.
IC = "IC", risk = "asBias", neighbor = "ContNeighborhood", L2Fam = "missing": asymptotic bias of IC under convex contaminations.
IC = "IC", risk = "asBias", neighbor = "ContNeighborhood", L2Fam = "L2ParamFamily": asymptotic bias of IC under convex contaminations and L2Fam.
IC = "IC", risk = "asBias", neighbor = "TotalVarNeighborhood", L2Fam = "missing": asymptotic bias of IC in case of total variation neighborhoods.
IC = "IC", risk = "asBias", neighbor = "TotalVarNeighborhood", L2Fam = "L2ParamFamily": asymptotic bias of IC under L2Fam in case of total variation neighborhoods.
IC = "IC", risk = "asMSE", neighbor = "UncondNeighborhood", L2Fam = "missing": asymptotic mean square error of IC.
IC = "IC", risk = "asMSE", neighbor = "UncondNeighborhood", L2Fam = "L2ParamFamily": asymptotic mean square error of IC under L2Fam.
IC = "TotalVarIC", risk = "asUnOvShoot", neighbor = "UncondNeighborhood", L2Fam = "missing": asymptotic under-/overshoot risk of IC.
IC = "IC", risk = "fiUnOvShoot", neighbor = "ContNeighborhood", L2Fam = "missing": finite-sample under-/overshoot risk of IC.
IC = "IC", risk = "fiUnOvShoot", neighbor = "TotalVarNeighborhood", L2Fam = "missing": finite-sample under-/overshoot risk of IC.

Details

To make sure that the results are valid, it is recommended to include an additional check of the IC properties of IC using checkIC.

References

Huber, P.J. (1968) Robust Confidence Limits. Z. Wahrscheinlichkeitstheor. Verw. Geb. 10:269--278.

Rieder, H. (1980) Estimates derived from robust tests. Ann. Stats. 8: 106--115.

Rieder, H. (1994) Robust Asymptotic Statistics. New York: Springer.

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

Ruckdeschel, P. and Kohl, M. (2005) Computation of the Finite Sample Risk of M-estimators on Neighborhoods.