# L2 differentiable parametric regression-type family

### Description

Class for L2 differentiable parametric regression-type families.

### Objects from the Class

Objects can be created by calls of the form `new("L2RegTypeFamily", ...)`

.
More frequently they are created via the generating function
`L2RegTypeFamily`

.

### Slots

`L2deriv`

:Object of class

`"EuclRandVarList"`

: L2 derivative.`ErrorL2deriv`

:Object of class

`"EuclRandVarList"`

: L2 derivative of`ErrorDistr`

.`ErrorL2derivSymm`

:Object of class

`"FunSymmList"`

: symmetry of`ErrorL2deriv`

.`ErrorL2derivDistr`

:Object of class

`"DistrList"`

: distribution of`ErrorL2deriv`

.`ErrorL2derivDistrSymm`

:Object of class

`"DistrSymmList"`

: symmetry of`ErrorL2derivDistr`

.`FisherInfo`

:Object of class

`"PosDefSymmMatrix"`

: Fisher information.`ErrorDistr`

:Object of class

`"Distribution"`

: error distribution.`ErrorSymm`

:Object of class

`"DistributionSymmetry"`

: symmetry of`ErrorDistr`

.`RegDistr`

:Object of class

`"Distribution"`

: regressor distribution.`RegSymm`

:Object of class

`"DistributionSymmetry"`

: symmetry of`RegDistr`

.`Regressor`

:Object of class

`"EuclRandVariable"`

: regressor.`param`

:Object of class

`"ParamFamParameter"`

: parameter of the family.`props`

:Object of class

`"character"`

: properties of the family.`name`

:Object of class

`"character"`

: name of the family.`distribution`

:Object of class

`"CondDistribution"`

: conditional distribution given the regressor.`distrSymm`

:Object of class

`"DistributionSymmetry"`

: symmetry of`distribution`

.

### Extends

Class `"RegTypeFamily"`

, directly.

Class `"ParamFamily"`

, by class `"RegTypeFamily"`

.

Class `"ProbFamily"`

, by class `"RegTypeFamily"`

.

### Methods

- L2deriv
`signature(object = "L2RegTypeFamily")`

: acessor function for slot`L2deriv`

- FisherInfo
`signature(object = "L2RegTypeFamily")`

: acessor function for slot`FisherInfo`

- ErrorL2deriv
`signature(object = "L2RegTypeFamily")`

: acessor function for slot`ErrorL2deriv`

.- ErrorL2derivDistr
`signature(object = "L2RegTypeFamily")`

: acessor function for slot`ErrorL2derivDistr`

.- ErrorL2derivSymm
`signature(object = "L2RegTypeFamily")`

: acessor function for slot`ErrorL2derivSymm`

- ErrorL2derivDistrSymm
`signature(object = "L2RegTypeFamily")`

: acessor function for slot`ErrorL2derivDistrSymm`

- checkL2deriv
`signature(object = "L2RegTypeFamily")`

: check centering of`L2deriv`

and compute precision of Fisher information.- checkIC
`signature(IC = "IC", L2Fam = "missing")`

: check centering and Fisher consistency of`IC`

assuming the L2-differentiable regression-type family which can be created via the slot`CallL2Fam`

of`IC`

.- checkIC
`signature(IC = "IC", L2Fam = "L2RegTypeFamily")`

: check centering and Fisher consistency of`IC`

assuming the L2-differentiable regression-type family`L2Fam`

.- E
`signature(object = "L2RegTypeFamily", fun = "EuclRandVariable", cond = "missing")`

: expectation of`fun`

under`object`

.- E
`signature(object = "L2RegTypeFamily", fun = "EuclRandMatrix", cond = "missing")`

: expectation of`fun`

under`object`

.- E
`signature(object = "L2RegTypeFamily", fun = "EuclRandVarList", cond = "missing")`

: expectation of`fun`

under`object`

.- show
`signature(object = "L2RegTypeFamily")`

### Author(s)

Matthias Kohl Matthias.Kohl@stamats.de

### References

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

### See Also

`RegTypeFamily-class`

### Examples

1 | ```
new("L2RegTypeFamily")
``` |

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