# getReq -- computation of the radius interval where IC1 is better than IC2. (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. ```r getReq(Risk,neighbor,IC1,IC2,n=1,upper=15, radOrOutl=c("radius","Outlier"), ...) ``` ## Arguments - `Risk`: an object of class `"asGRisk"` -- the risk at which IC1 is better than IC2. - `neighbor`: object of class `"Neighborhood"`; the neighborhood at which to compute the bias. - `IC1`: some IC of class `"IC"` - `IC2`: some IC of class `"IC"` - `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 `E()`. ## Returns 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`. ## References Hampel et al. (1986) **Robust Statistics**. The Approach Based on Influence Functions. New York: Wiley. Rieder, H. (1994) **Robust Asymptotic Statistics**. New York: Springer. ## Author(s) Peter Ruckdeschel peter.ruckdeschel@fraunhofer.itwm.de ## Examples ```r 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) ```

getReq function