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**distrMod**: Object Oriented Implementation of Probability Models**QFnorm-class**: Norm classes for norms based on quadratic forms

# Norm classes for norms based on quadratic forms

### Description

Classes for norms based on quadratic forms

### Objects from the Class

could be created by a call to `new`

, but
normally one would use the generating functions `QFNorm`

,
`InfoNorm`

, and `SelfNorm`

### Slots

`name`

Object of class

`"character"`

.`fct`

Object of class

`"function"`

.`QuadForm`

Object of class

`"PosSemDefSymmMatrix"`

.

### Extends

`"QFNorm"`

extends class `"NormType"`

, directly,
and `"InfoNorm"`

and `"SelfNorm"`

each extend
class `"QFNorm"`

, directly (and do not have extra slots).

### Methods

- QuadForm
`signature(object = "QFNorm")`

: accessor function for slot`QuadForm`

.- QuadForm<-
`signature(object = "QFNorm")`

: replacement function for slot`QuadForm`

.

### Author(s)

Peter Ruckdeschel peter.ruckdeschel@uni-oldenburg.de

### References

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

Ruckdeschel, P. and Rieder, H. (2004) Optimal Influence Curves for
General Loss Functions. Statistics & Decisions *22*, 201-223.

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

### See Also

`NormType-class`

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- 0distrMod-package: distrMod - Object Oriented Implementation of Probability...
- addAlphTrsp2col: "addAlphTrsp2col"
- asBias: Generating function for asBias-class
- asBias-class: Standardized Asymptotic Bias
- asCov: Generating function for asCov-class
- asCov-class: Asymptotic covariance
- asGRisk-class: Convex asymptotic risk
- asHampel: Generating function for asHampel-class
- asHampel-class: Asymptotic Hampel risk
- asMSE: Generating function for asMSE-class
- asMSE-class: Asymptotic mean square error
- asRisk-class: Aymptotic risk
- asRiskwithBias-class: Aymptotic risk
- asSemivar: Generating function for asSemivar-class
- asSemivar-class: Semivariance Risk Type
- asUnOvShoot: Generating function for asUnOvShoot-class
- asUnOvShoot-class: Asymptotic under-/overshoot probability
- asymmetricBias: Generating function for asymmetricBias-class
- asymmetricBias-class: asymmetric Bias Type
- BetaFamily: Generating function for Beta families
- BiasType-class: Bias Type
- BinomFamily: Generating function for Binomial families
- CauchyLocationScaleFamily: Generating function for Cauchy location and scale families
- checkL2deriv: Generic function for checking L2-derivatives
- Confint-class: Confint-class
- confint-methods: Methods for function confint in Package 'distrMod'
- distrModMASK: Masking of/by other functions in package "distrMod"
- distrModOptions: Function to change the global variables of the package...
- Estimate-class: Estimate-class.
- Estimator: Function to compute estimates
- EvenSymmetric: Generating function for EvenSymmetric-class
- EvenSymmetric-class: Class for Even Functions
- existsPIC: Methods for Function existsPIC in Package 'distrMod'
- ExpScaleFamily: Generating function for exponential scale families
- fiBias: Generating function for fiBias-class
- fiBias-class: Finite-sample Bias
- fiCov: Generating function for fiCov-class
- fiCov-class: Finite-sample covariance
- fiHampel: Generating function for fiHampel-class
- fiHampel-class: Finite-sample Hampel risk
- fiMSE: Generating function for fiMSE-class
- fiMSE-class: Finite-sample mean square error
- fiRisk-class: Finite-sample risk
- fiUnOvShoot: Generating function for fiUnOvShoot-class
- fiUnOvShoot-class: Finite-sample under-/overshoot probability
- FunctionSymmetry-class: Class of Symmetries for Functions
- FunSymmList: Generating function for FunSymmList-class
- FunSymmList-class: List of Symmetries for a List of Functions
- GammaFamily: Generating function for Gamma families
- InfoNorm: Generating function for InfoNorm-class
- internalClassUnions-class: Class unions in 'distrMod'
- internal-methods: Methods for Function .checkEstClassForParamFamily in Package...
- internalmleHelpers: Internal helper functions for treating MCEstimators in...
- InternalReturnClasses-class: Internal return classes for generating functions
- internals: Internal functions of package distrMod
- internals-qqplot: Internal functions for qqplot of package distrMod
- isKerAinKerB: isKerAinKerB
- L2GroupFamily-class: L2 differentiable parametric group family
- L2LocationFamily: Generating function for L2LocationFamily-class
- L2LocationFamily-class: L2 differentiable parametric group family
- L2LocationScaleFamily: Generating function for L2LocationScaleFamily-class
- L2LocationScaleFamily-class: L2 differentiable parametric group family
- L2LocationUnknownScaleFamily: Generating function for L2LocationScaleFamily-class in...
- L2ParamFamily: Generating function for L2ParamFamily-class
- L2ParamFamily-class: L2 differentiable parametric family
- L2ScaleFamily: Generating function for L2ScaleFamily-class
- L2ScaleFamily-class: L2 differentiable parametric group family
- L2ScaleUnknownLocationFamily: Generating function for L2LocationScaleFamily-class in...
- LnormScaleFamily: Generating function for lognormal scale families
- MCEstimate-class: MCEstimate-class.
- MCEstimator: Function to compute minimum criterion estimates
- MDEstimator: Function to compute minimum distance estimates
- meRes: helper functions for mceCalc and mleCalc
- mleCalc-methods: Methods for functions mceCalc and mleCalc in Package...
- MLEstimator: Function to compute maximum likelihood estimates
- modifyModel-methods: Methods for function modifyModel in Package 'distrMod'
- NBinomFamily: Generating function for Nbinomial families
- negativeBias: Generating function for onesidedBias-class
- NonSymmetric: Generating function for NonSymmetric-class
- NonSymmetric-class: Class for Non-symmetric Functions
- NormLocationFamily: Generating function for normal location families
- NormLocationScaleFamily: Generating function for normal location and scale families
- NormLocationUnknownScaleFamily: Generating function for normal location families with unknown...
- norms: Norm functions
- NormScaleFamily: Generating function for normal scale families
- NormScaleUnknownLocationFamily: Generating function for normal scale families with unknown...
- NormType: Generating function for NormType-class
- NormType-class: Norm Type
- OddSymmetric: Generating function for OddSymmetric-class
- OddSymmetric-class: Class for Odd Functions
- onesidedBias-class: onesided Bias Type
- ParamFamily: Generating function for ParamFamily-class
- ParamFamily-class: Parametric family of probability measures.
- ParamFamParameter: Generating function for ParamFamParameter-class
- ParamFamParameter-class: Parameter of a parametric family of probability measures
- PoisFamily: Generating function for Poisson families
- positiveBias: Generating function for onesidedBias-class
- print-methods: Common 'print' Methods for S4 classes in Package 'distrMod'
- ProbFamily-class: Family of probability measures
- QFNorm: Generating function for QFNorm-class
- QFnorm-class: Norm classes for norms based on quadratic forms
- qqplot: Methods for Function qqplot in Package 'distrMod'
- returnlevelplot: Methods for Function returnlevelplot in Package 'distrMod'
- RiskType-class: Risk
- SelfNorm: Generating function for SelfNorm-class
- symmetricBias: Generating function for symmetricBias-class
- symmetricBias-class: symmetric Bias Type
- trafoEst: Function trafoEst in Package 'distrMod'
- trafo-methods: Methods for function trafo in Package 'distrMod'
- trAsCov: Generating function for trAsCov-class
- trAsCov-class: Trace of asymptotic covariance
- trFiCov: Generating function for trFiCov-class
- trFiCov-class: Trace of finite-sample covariance
- validParameter-methods: Methods for function validParameter in Package 'distrMod'