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).

- 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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