getInfGamma | R Documentation |

Generic function for the computation of the optimal clipping bound.
This function is rarely called directly. It is called by `getInfClip`

to compute optimally robust ICs.

```
getInfGamma(L2deriv, risk, neighbor, biastype, ...)
## S4 method for signature
## 'UnivariateDistribution,asGRisk,ContNeighborhood,BiasType'
getInfGamma(L2deriv,
risk, neighbor, biastype, cent, clip)
## S4 method for signature
## 'UnivariateDistribution,asGRisk,TotalVarNeighborhood,BiasType'
getInfGamma(L2deriv,
risk, neighbor, biastype, cent, clip)
## S4 method for signature 'RealRandVariable,asMSE,ContNeighborhood,BiasType'
getInfGamma(L2deriv,
risk, neighbor, biastype, Distr, stand, cent, clip, power = 1L, ...)
## S4 method for signature
## 'RealRandVariable,asMSE,TotalVarNeighborhood,BiasType'
getInfGamma(L2deriv,
risk, neighbor, biastype, Distr, stand, cent, clip, power = 1L, ...)
## S4 method for signature
## 'UnivariateDistribution,asUnOvShoot,ContNeighborhood,BiasType'
getInfGamma(L2deriv,
risk, neighbor, biastype, cent, clip)
## S4 method for signature
## 'UnivariateDistribution,asMSE,ContNeighborhood,onesidedBias'
getInfGamma(L2deriv,
risk, neighbor, biastype, cent, clip)
## S4 method for signature
## 'UnivariateDistribution,asMSE,ContNeighborhood,asymmetricBias'
getInfGamma(L2deriv,
risk, neighbor, biastype, cent, clip)
```

`L2deriv` |
L2-derivative of some L2-differentiable family of probability measures. |

`risk` |
object of class |

`neighbor` |
object of class |

`biastype` |
object of class |

`...` |
additional parameters, in particular for expectation |

`cent` |
optimal centering constant. |

`clip` |
optimal clipping bound. |

`stand` |
standardizing matrix. |

`Distr` |
object of class |

`power` |
exponent for the integrand; by default |

The function is used in case of asymptotic G-risks; confer Ruckdeschel and Rieder (2004).

The optimal clipping height is computed. More specifically, the optimal
clipping height `b`

is determined in a zero search of a certain function
`\gamma`

, where the respective `getInf`

-method will return
the value of `\gamma(b)`

. The actual function `\gamma`

varies according to whether the parameter is one dimensional or higher dimensional,
according to the risk, according to the neighborhood, and according to the
bias type, which leads to the different methods.

- L2deriv = "UnivariateDistribution", risk = "asGRisk", neighbor = "ContNeighborhood", biastype = "BiasType"
used by

`getInfClip`

for symmetric bias.- L2deriv = "UnivariateDistribution", risk = "asGRisk", neighbor = "TotalVarNeighborhood", biastype = "BiasType"
used by

`getInfClip`

for symmetric bias.- L2deriv = "RealRandVariable", risk = "asMSE", neighbor = "ContNeighborhood", biastype = "BiasType"
used by

`getInfClip`

for symmetric bias.- L2deriv = "RealRandVariable", risk = "asMSE", neighbor = "TotalVarNeighborhood", biastype = "BiasType"
used by

`getInfClip`

for symmetric bias.- L2deriv = "UnivariateDistribution", risk = "asUnOvShoot", neighbor = "ContNeighborhood", biastype = "BiasType"
used by

`getInfClip`

for symmetric bias.- L2deriv = "UnivariateDistribution", risk = "asMSE", neighbor = "ContNeighborhood", biastype = "onesidedBias"
used by

`getInfClip`

for onesided bias.- L2deriv = "UnivariateDistribution", risk = "asMSE", neighbor = "ContNeighborhood", biastype = "asymmetricBias"
used by

`getInfClip`

for asymmetric bias.

Matthias Kohl Matthias.Kohl@stamats.de, Peter Ruckdeschel peter.ruckdeschel@uni-oldenburg.de

Rieder, H. (1980) Estimates derived from robust tests. Ann. Stats. **8**: 106–115.

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.

Ruckdeschel, P. (2005) Optimally One-Sided Bounded Influence Curves.
Mathematical Methods in Statistics *14*(1), 105-131.

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

`asGRisk-class`

, `asMSE-class`

,
`asUnOvShoot-class`

, `ContIC-class`

,
`TotalVarIC-class`

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