Description Usage Arguments Value Author(s) References Examples

(tries to) compute a radius interval where IC1 is better than IC2, respectively the number of (worst-case) outliers interval where IC1 is better than IC2.

1 |

`Risk` |
an object of class |

`neighbor` |
object of class |

`IC1` |
some IC of class |

`IC2` |
some IC of class |

`n` |
the sample size; by default set to 1; then the radius interval refers to starting radii in the shrinking neighborhood setting of Rieder[94]. Otherwise the radius interval is scaled down accordingly. |

`upper` |
the upper bound of the radius interval in which to search |

`radOrOutl` |
a character string specifying whether an interval of radii or a number of outliers is returned; must be one of "radius" (default) and "Outlier". |

`...` |
further arguments to be passed on |

The radius interval (given by its endpoints) where `IC1`

is better than `IC2`

according to the risk. In case `IC2`

is better than `IC1`

as to both variance and bias,
the return value is `NA`

.

Peter Ruckdeschel [email protected]

Hampel et al. (1986) *Robust Statistics*.
The Approach Based on Influence Functions. New York: Wiley.

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

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 | ```
N0 <- NormLocationFamily(mean=2, sd=3)
## L_2 family + infinitesimal neighborhood
neighbor <- ContNeighborhood(radius = 0.5)
N0.Rob1 <- InfRobModel(center = N0, neighbor = neighbor)
## OBRE solution (ARE 95%)
N0.ICA <- optIC(model = N0.Rob1, risk = asAnscombe(.95))
## MSE solution
N0.ICM <- optIC(model=N0.Rob1, risk=asMSE())
getReq(asMSE(),neighbor,N0.ICA,N0.ICM,n=1)
getReq(asMSE(),neighbor,N0.ICA,N0.ICM,n=30)
## Don't test to reduce check time on CRAN
## RMX solution
N0.ICR <- radiusMinimaxIC(L2Fam=N0, neighbor=neighbor,risk=asMSE())
getReq(asL1(),neighbor,N0.ICA,N0.ICM,n=30)
getReq(asL4(),neighbor,N0.ICA,N0.ICM,n=30)
getReq(asMSE(),neighbor,N0.ICA,N0.ICR,n=30)
getReq(asL1(),neighbor,N0.ICA,N0.ICR,n=30)
getReq(asL4(),neighbor,N0.ICA,N0.ICR,n=30)
getReq(asMSE(),neighbor,N0.ICM,N0.ICR,n=30)
### when to use MAD and when Qn
## for Qn, see C. Croux, P. Rousseeuw (1993). Alternatives to the Median
## Absolute Deviation, JASA 88(424):1273-1283
L2M <- NormScaleFamily()
IC.mad <- makeIC(function(x)sign(abs(x)-qnorm(.75)),L2M)
d.qn <- (2^.5*qnorm(5/8))^-1
IC.qn <- makeIC(function(x) d.qn*(1/4 - pnorm(x+1/d.qn) + pnorm(x-1/d.qn)), L2M)
getReq(asMSE(), neighbor, IC.mad, IC.qn)
getReq(asMSE(), neighbor, IC.mad, IC.qn, radOrOutl = "Outlier", n = 30)
# => MAD is better once r > 0.5144 (i.e. for more than 2 outliers for n = 30)
``` |

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