# Conditionally centered influence curve of total variaton type

### Description

Class of conditionally centered (partial) influence
curves of contamination type for average conditional total variation
neighborhoods; i.e., influence curves *eta* of the form

*
eta = A x Lambda_f min(1, max(c(x)/(|Ax|Lambda_f), (c(x) + b)/(|Ax|Lambda_f)))*

with lower clipping function *c*, standardized bias *b* and
standardizing matrix *A*. *Lambda_f* stands for
the L2 derivative of the corresponding error distribution.

### Objects from the Class

Objects can be created by calls of the form `new("Av1CondTotalVarIC", ...)`

.
More frequently they are created via the generating function
`Av1CondTotalVarIC`

, respectively via the method `generateIC`

.

### Slots

`CallL2Fam`

:object of class

`"call"`

: creates an object of the underlying L2-differentiable regression type 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.`clipUp`

:object of class

`"numeric"`

: standardized bias.`clipLo`

:object of class

`"RealRandVariable"`

: lower clipping function.`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 average conditional contamination neighborhood.

### Extends

Class `"CondIC"`

, directly.
Class `"IC"`

, by class `"CondIC"`

.
Class `"InfluenceCurve"`

, by class `"CondIC"`

.

### Methods

- CallL2Fam<-
`signature(object = "Av1CondTotalVarIC")`

: replacement function for slot`CallL2Fam`

.- clipLo
`signature(object = "Av1CondTotalVarIC")`

: accessor function for slot`clipLo`

.- clipLo<-
`signature(object = "Av1CondTotalVarIC")`

: replacement function for slot`clipLo`

.- clipUp
`signature(object = "Av1CondTotalVarIC")`

: accessor function for slot`clipUp`

.- clipUp<-
`signature(object = "Av1CondTotalVarIC")`

: replacement function for slot`clipUp`

.- stand
`signature(object = "Av1CondTotalVarIC")`

: accessor function for slot`stand`

.- stand<-
`signature(object = "Av1CondTotalVarIC")`

: replacement function for slot`stand`

.- lowerCase
`signature(object = "Av1CondTotalVarIC")`

: accessor function for slot`lowerCase`

.- lowerCase<-
`signature(object = "Av1CondTotalVarIC")`

: replacement function for slot`lowerCase`

.- neighborRadius
`signature(object = "Av1CondTotalVarIC")`

: accessor function for slot`neighborRadius`

.- neighborRadius<-
`signature(object = "Av1CondTotalVarIC")`

: replacement function for slot`neighborRadius`

.- generateIC
`signature(neighbor = "Av1CondTotalVarNeighborhood", L2Fam = "L2RegTypeFamily")`

: generate an object of class`"Av1CondTotalVarIC"`

. Rarely called directly.- show
`signature(object = "Av1CondTotalVarIC")`

### 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

`CondIC-class`

, `Av1CondTotalVarIC`

### Examples

1 2 | ```
IC1 <- new("Av1CondTotalVarIC")
IC1
``` |