radiusMinimaxIC {ROptEst} | R Documentation |
Generic function for the computation of the radius minimax IC.
radiusMinimaxIC(L2Fam, neighbor, risk, ...) ## S4 method for signature 'L2ParamFamily, ## UncondNeighborhood, asGRisk': radiusMinimaxIC( L2Fam, neighbor, risk, loRad, upRad, z.start = NULL, A.start = NULL, upper = 1e5, maxiter = 50, tol = .Machine$double.eps^0.4, warn = FALSE, verbose = FALSE)
L2Fam |
L2-differentiable family of probability measures. |
neighbor |
object of class "Neighborhood" . |
risk |
object of class "RiskType" . |
... |
additional parameters. |
loRad |
the lower end point of the interval to be searched. |
upRad |
the upper end point of the interval to be searched. |
z.start |
initial value for the centering constant. |
A.start |
initial value for the standardizing matrix. |
upper |
upper bound for the optimal clipping bound. |
maxiter |
the maximum number of iterations |
tol |
the desired accuracy (convergence tolerance). |
warn |
logical: print warnings. |
verbose |
logical: if TRUE , some messages are printed |
In case the neighborhood radius is unknown, Rieder et al. (2001, 2008) and Kohl (2005) show that there is nevertheless a way to compute an optimally robust IC - the so-called radius-minimax IC - which is optimal for some radius interval.
The radius minimax IC is computed.
Matthias Kohl Matthias.Kohl@stamats.de, Peter Ruckdeschel Peter.Ruckdeschel@itwm.fraunhofer.de
Rieder, H., Kohl, M. and Ruckdeschel, P. (2008) The Costs of not Knowing the Radius. Statistical Methods and Applications, 17(1) 13-40.
Rieder, H., Kohl, M. and Ruckdeschel, P. (2001) The Costs of not Knowing the Radius. Appeared as discussion paper Nr. 81. SFB 373 (Quantification and Simulation of Economic Processes), Humboldt University, Berlin; also available under www.uni-bayreuth.de/departments/math/org/mathe7/RIEDER/pubs/RR.pdf
Kohl, M. (2005) Numerical Contributions to the Asymptotic Theory of Robustness. Bayreuth: Dissertation.
N <- NormLocationFamily(mean=0, sd=1) radIC <- radiusMinimaxIC(L2Fam=N, neighbor=ContNeighborhood(), risk=asMSE(), loRad=0.1, upRad=0.5) checkIC(radIC)