Description

Class of (partial) influence curves of total variation type. i.e., an influence curves eta of the form

eta = max(c, min(A Lambda, d))

with lower clipping bound c, upper clipping bound d and standardizing matrix A. Lambda stands for the L2 derivative of the corresponding L2 differentiable parametric family which can be created via CallL2Fam.

Objects from the Class

Objects can be created by calls of the form new("TotalVarIC", ...). More frequently they are created via the generating function TotalVarIC, respectively via the method generateIC.

Slots

CallL2Fam:

object of class "call": creates an object of the underlying L2-differentiable parametric family.

name:

object of class "character".

Curve:

object of class "EuclRandVarList".

Risks:

object of class "list": list of risks; cf. RiskType-class.

Infos:

object of class "matrix" with two columns named method and message: additional informations.

clipLo:

object of class "numeric": lower clipping bound.

clipUp:

object of class "numeric": upper clipping bound.

stand:

object of class "matrix": standardizing matrix.

lowerCase

object of class "OptionalNumeric": optional constant for lower case solution.

neighborRadius:

object of class "numeric": radius of the corresponding (unconditional) contamination neighborhood.

Extends

Class "IC", directly.
Class "InfluenceCurve", by class "IC".

Methods

CallL2Fam<-

signature(object = "TotalVarIC"): replacement function for slot CallL2Fam.

clipLo

signature(object = "TotalVarIC"): accessor function for slot clipLo.

clipLo<-

signature(object = "TotalVarIC"): replacement function for slot clipLo.

clipUp

signature(object = "TotalVarIC"): accessor function for slot clipUp.

clipUp<-

signature(object = "TotalVarIC"): replacement function for slot clipUp.

stand

signature(object = "TotalVarIC"): accessor function for slot stand.

stand<-

signature(object = "TotalVarIC"): replacement function for slot stand.

neighborRadius

signature(object = "TotalVarIC"): accessor function for slot neighborRadius.

neighborRadius<-

signature(object = "TotalVarIC"): replacement function for slot neighborRadius.

generateIC

signature(neighbor = "TotalVarNeighborhood", L2Fam = "L2ParamFamily"): generate an object of class "TotalVarIC". Rarely called directly.

show

signature(object = "TotalVarIC")

Author(s)

Matthias Kohl Matthias.Kohl@stamats.de

References

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

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

See Also

IC-class, ContIC

Examples