Description Objects from the Class Slots Extends Methods Author(s) References See Also Examples

Class of L2 differentiable parametric group families.

Objects can be created by calls of the form `new("L2ScaleFamily", ...)`

.
More frequently they are created via the generating function
`L2ScaleFamily`

.

`name`

[inherited from class

`"ProbFamily"`

] object of class`"character"`

: name of the family.`distribution`

[inherited from class

`"ProbFamily"`

] object of class`"Distribution"`

: member of the family.`distrSymm`

[inherited from class

`"ProbFamily"`

] object of class`"DistributionSymmetry"`

: symmetry of`distribution`

.`param`

[inherited from class

`"ParamFamily"`

] object of class`"ParamFamParameter"`

: parameter of the family.`fam.call`

[inherited from class

`"ParamFamily"`

] object of class`"call"`

: call by which parametric family was produced.`makeOKPar`

[inherited from class

`"ParamFamily"`

] object of class`"function"`

: has argument`param`

— the (total) parameter, returns valid parameter; used if`optim`

resp.`optimize`

— try to use “illegal” parameter values; then`makeOKPar`

makes a valid parameter value out of the illegal one.`startPar`

[inherited from class

`"ParamFamily"`

] object of class`"function"`

: has argument`x`

— the data, returns starting parameter for`optim`

resp.`optimize`

— a starting estimator in case parameter is multivariate or a search interval in case parameter is univariate.`modifyParam`

[inherited from class

`"ParamFamily"`

] object of class`"function"`

: mapping from the parameter space (represented by`"param"`

) to the distribution space (represented by`"distribution"`

).`props`

[inherited from class

`"ProbFamily"`

] object of class`"character"`

: properties of the family.`L2deriv`

[inherited from class

`"L2ParamFamily"`

] object of class`"EuclRandVariable"`

: L2 derivative of the family.`L2deriv.fct`

[inherited from class

`"L2ParamFamily"`

] object of class`"function"`

: mapping from the parameter space (argument`param`

of class`"ParamFamParameter"`

) to a mapping from observation`x`

to the value of the L2derivative;`L2deriv.fct`

is then used from observation`x`

to value of the L2derivative;`L2deriv.fct`

is used by`modifyModel`

to move the L2deriv according to a change in the parameter`L2derivSymm`

[inherited from class

`"L2ParamFamily"`

] object of class`"FunSymmList"`

: symmetry of the maps included in`L2deriv`

.`L2derivDistr`

[inherited from class

`"L2ParamFamily"`

] object of class`"UnivarDistrList"`

: list which includes the distribution of`L2deriv`

.`L2derivDistrSymm`

[inherited from class

`"L2ParamFamily"`

] object of class`"DistrSymmList"`

: symmetry of the distributions included in`L2derivDistr`

.`FisherInfo.fct`

[inherited from class

`"L2ParamFamily"`

] object of class`"function"`

: mapping from the parameter space (argument`param`

of class`"ParamFamParameter"`

) to the set of positive semidefinite matrices;`FisherInfo.fct`

is used by`modifyModel`

to move the Fisher information according to a change in the parameter`FisherInfo`

[inherited from class

`"L2ParamFamily"`

] object of class`"PosDefSymmMatrix"`

: Fisher information of the family.`LogDeriv`

[inherited from class

`"L2GroupParamFamily"`

] object of class`"function"`

: has argument`x`

; the negative logarithmic derivative of the density of the model distribution at the "standard" parameter value.`locscalename`

[inherited from class

`"L2LocationScaleUnion"`

] object of class`"character"`

: names of location and scale parameter

Class `"L2LocationScaleUnion"`

, directly.

Class `"L2GroupParamFamily"`

, by class `"L2LocationScaleUnion"`

.

Class `"L2ParamFamily"`

, by class `"L2GroupParamFamily"`

.

Class `"ParamFamily"`

, by class `"L2ParamFamily"`

.

Class `"ProbFamily"`

, by class `"ParamFamily"`

.

- modifyModel
`signature(model = "L2ScaleFamily", param = "ParamFamParameter")`

: moves the L2-scale family`model`

to parameter`param`

Matthias Kohl [email protected],

Peter Ruckdeschel [email protected]

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

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

`L2ScaleFamily`

, `ParamFamily-class`

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