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 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
.
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
by makeIC
, and (4) ...
for arguments to be passed to
calls to E
in makeIC
. 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 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.
weight
object of class "BdStWeight"
:
weight function
biastype
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.
Class "HampIC"
, directly.
Class "IC"
, by class "HampIC"
.
Class "InfluenceCurve"
, by class "IC"
.
signature(object = "TotalVarIC")
:
replacement function for slot CallL2Fam
.
signature(object = "TotalVarIC")
:
accessor function for slot clipLo
.
signature(object = "TotalVarIC")
:
replacement function for slot clipLo
.
signature(object = "TotalVarIC")
:
accessor function for slot clipUp
.
signature(object = "TotalVarIC")
:
replacement function for slot clipUp
.
signature(x1 = "TotalVarIC")
:
returns clipUp-clipLo
.
signature(object = "TotalVarIC")
:
replacement function for slot stand
.
signature(object = "TotalVarIC")
:
replacement function for slot lowerCase
.
signature(object = "TotalVarIC")
:
generates an object of class "TotalVarNeighborhood"
with
radius given in slot neighborRadius
.
signature(neighbor = "TotalVarNeighborhood", L2Fam = "L2ParamFamily")
:
generate an object of class "TotalVarIC"
. Rarely called directly.
signature(object = "TotalVarIC")
Matthias Kohl Matthias.Kohl@stamats.de
Rieder, H. (1994) Robust Asymptotic Statistics. New York: Springer.
Kohl, M. (2005) Numerical Contributions to the Asymptotic Theory of Robustness. Bayreuth: Dissertation.
IC-class
, ContIC
, HampIC-class
IC1 <- new("TotalVarIC")
plot(IC1)
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