L2ScaleFamily-class {distrMod}

L2 differentiable parametric group family

Description

Class of L2 differentiable parametric group families.

Objects from the Class

Objects can be created by calls of the form new("L2ScaleFamily", ...). More frequently they are created via the generating function L2ScaleFamily.

Slots

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

Extends

Class "L2LocationScaleUnion", directly.
Class "L2GroupParamFamily", by class "L2LocationScaleUnion".
Class "L2ParamFamily", by class "L2GroupParamFamily".
Class "ParamFamily", by class "L2ParamFamily".
Class "ProbFamily", by class "ParamFamily".

Methods

modifyModel

signature(model = "L2ScaleFamily", param = "ParamFamParameter"): moves the L2-scale family model to parameter param

Author(s)

Matthias Kohl [e-mail],
Peter Ruckdeschel [e-mail]

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

L2ScaleFamily, ParamFamily-class

Examples

F1 <- new("L2ScaleFamily")
plot(F1)