TotalVarIC-class {RobAStBase} | R Documentation |
Influence curve of total variation type
Description
Class of (partial) influence curves of total variation type.
i.e., an influence curves \eta
of the form
\eta = c \vee A\Lambda \wedge 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"
.modifyIC
object of class
"OptionalFunction"
: function of four arguments: (1)L2Fam
an L2 parametric family (2)IC
an optional influence curve, (3)withMakeIC
a logical argument whether to enforce the IC side conditions bymakeIC
, and (4)...
for arguments to be passed to calls toE
inmakeIC
. Returns an object of class"IC"
. This function is mainly used for internal computations!Risks
object of class
"list"
: list of risks; cf.RiskType-class
.Infos
object of class
"matrix"
with two columns namedmethod
andmessage
: 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.weight
object of class
"BdStWeight"
: weight functionbiastype
object of class
"BiasType"
: bias type (symmetric/onsided/asymmetric)normtype
object of class
"NormType"
: norm type (Euclidean, information/self-standardized)neighborRadius
object of class
"numeric"
: radius of the corresponding (unconditional) contamination neighborhood.
Extends
Class "HampIC"
, directly.
Class "IC"
, by class "HampIC"
.
Class "InfluenceCurve"
, by class "IC"
.
Methods
- CallL2Fam<-
signature(object = "TotalVarIC")
: replacement function for slotCallL2Fam
.- clipLo
signature(object = "TotalVarIC")
: accessor function for slotclipLo
.- clipLo<-
signature(object = "TotalVarIC")
: replacement function for slotclipLo
.- clipUp
signature(object = "TotalVarIC")
: accessor function for slotclipUp
.- clipUp<-
signature(object = "TotalVarIC")
: replacement function for slotclipUp
.- clip
signature(x1 = "TotalVarIC")
: returnsclipUp-clipLo
.- stand<-
signature(object = "TotalVarIC")
: replacement function for slotstand
.- lowerCase<-
signature(object = "TotalVarIC")
: replacement function for slotlowerCase
.- neighbor
signature(object = "TotalVarIC")
: generates an object of class"TotalVarNeighborhood"
with radius given in slotneighborRadius
.- 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
, HampIC-class
Examples
IC1 <- new("TotalVarIC")
plot(IC1)