getRiskIC {RobAStBase}

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 signature 'IC,asCov,missing,missing'
getRiskIC(IC, risk,
    tol = .Machine$double.eps^0.25, withCheck = TRUE, ...)

## S4 method for signature 'IC,asCov,missing,L2ParamFamily'
getRiskIC(IC, risk, L2Fam,
    tol = .Machine$double.eps^0.25, withCheck = TRUE, ..., diagnostic = FALSE)

## S4 method for signature 'IC,trAsCov,missing,missing'
getRiskIC(IC, risk,
    tol = .Machine$double.eps^0.25, withCheck = TRUE, ...)

## S4 method for signature 'IC,trAsCov,missing,L2ParamFamily'
getRiskIC(IC, risk, L2Fam,
    tol = .Machine$double.eps^0.25, withCheck = TRUE, ...)

## S4 method for signature 'IC,asBias,UncondNeighborhood,missing'
getRiskIC(IC, risk, neighbor,
    tol = .Machine$double.eps^0.25, withCheck = TRUE, ...)

## S4 method for signature 'IC,asBias,UncondNeighborhood,L2ParamFamily'
getRiskIC(IC, risk, neighbor, L2Fam,
    tol = .Machine$double.eps^0.25, withCheck = TRUE, ...)

## S4 method for signature 'IC,asMSE,UncondNeighborhood,missing'
getRiskIC(IC, risk, neighbor,
    tol = .Machine$double.eps^0.25, withCheck = TRUE, ...)

## S4 method for signature 'IC,asMSE,UncondNeighborhood,L2ParamFamily'
getRiskIC(IC, risk, neighbor, L2Fam,
    tol = .Machine$double.eps^0.25, withCheck = TRUE, ...)

## S4 method for signature 'TotalVarIC,asUnOvShoot,UncondNeighborhood,missing'
getRiskIC(IC, risk, neighbor)

## S4 method for signature 'IC,fiUnOvShoot,ContNeighborhood,missing'
getRiskIC(IC, risk, neighbor, sampleSize, Algo = "A", cont = "left")

## S4 method for signature 'IC,fiUnOvShoot,TotalVarNeighborhood,missing'
getRiskIC(IC, risk, neighbor, sampleSize, Algo = "A", cont = "left")

Arguments

IC

object of class "InfluenceCurve"

risk

object of class "RiskType".

neighbor

object of class "Neighborhood".

L2Fam

object of class "L2ParamFamily".

...

additional parameters (e.g. to be passed to E).

tol

the desired accuracy (convergence tolerance).

sampleSize

integer: sample size.

Algo

"A" or "B".

cont

"left" or "right".

withCheck

logical: should a call to checkIC be done to check accuracy (defaults to TRUE).

diagnostic

logical; if TRUE, the return value obtains an attribute "diagnostic" with diagnostic information on the integration.

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.

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; uses method getBiasIC.

IC = "IC", risk = "asBias", neighbor = "ContNeighborhood", L2Fam = "L2ParamFamily"

asymptotic bias of IC under convex contaminations and L2Fam; uses method getBiasIC.

IC = "IC", risk = "asBias", neighbor = "TotalVarNeighborhood", L2Fam = "missing"

asymptotic bias of IC in case of total variation neighborhoods; uses method getBiasIC.

IC = "IC", risk = "asBias", neighbor = "TotalVarNeighborhood", L2Fam = "L2ParamFamily"

asymptotic bias of IC under L2Fam in case of total variation neighborhoods; uses method getBiasIC.

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.

Note

This generic function is still under construction.

Author(s)

Matthias Kohl [e-mail]
Peter Ruckdeschel [e-mail]

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.

See Also

getRiskIC, InfRobModel-class