getIneffDiff: Generic Function for the Computation of Inefficiency... In ROptEst: Optimally Robust Estimation

Description

Generic function for the computation of inefficiency differencies. This function is rarely called directly. It is used to compute the radius minimax IC and the least favorable radius.

Usage

 ```1 2 3 4 5 6 7 8``` ```getIneffDiff(radius, L2Fam, neighbor, risk, ...) ## S4 method for signature 'numeric,L2ParamFamily,UncondNeighborhood,asMSE' getIneffDiff( radius, L2Fam, neighbor, risk, loRad, upRad, loRisk, upRisk, z.start = NULL, A.start = NULL, upper.b = NULL, lower.b = NULL, OptOrIter = "iterate", MaxIter, eps, warn, loNorm = NULL, upNorm = NULL, verbose = NULL, ..., withRetIneff = FALSE) ```

Arguments

 `radius` neighborhood radius. `L2Fam` L2-differentiable family of probability measures. `neighbor` object of class `"Neighborhood"`. `risk` object of class `"RiskType"`. `loRad` the lower end point of the interval to be searched. `upRad` the upper end point of the interval to be searched. `loRisk` the risk at the lower end point of the interval. `upRisk` the risk at the upper end point of the interval. `z.start` initial value for the centering constant. `A.start` initial value for the standardizing matrix. `upper.b` upper bound for the optimal clipping bound. `lower.b` lower bound for the optimal clipping bound. `OptOrIter` character; which method to be used for determining Lagrange multipliers `A` and `a`: if (partially) matched to `"optimize"`, `getLagrangeMultByOptim` is used; otherwise: by default, or if matched to `"iterate"` or to `"doubleiterate"`, `getLagrangeMultByIter` is used. More specifically, when using `getLagrangeMultByIter`, and if argument `risk` is of class `"asGRisk"`, by default and if matched to `"iterate"` we use only one (inner) iteration, if matched to `"doubleiterate"` we use up to `Maxiter` (inner) iterations. `MaxIter` the maximum number of iterations `eps` the desired accuracy (convergence tolerance). `warn` logical: print warnings. `loNorm` object of class `"NormType"`; used in selfstandardization to evaluate the bias of the current IC in the norm of the lower bound `upNorm` object of class `"NormType"`; used in selfstandardization to evaluate the bias of the current IC in the norm of the upper bound `verbose` logical: if `TRUE`, some messages are printed `...` further arguments to be passed on to `getInfRobIC` `withRetIneff` logical: if `TRUE`, `getIneffDiff` returns the vector of lower and upper inefficiency (components named "lo" and "up"), otherwise (default) the difference. The latter was used in `radiusMinimaxIC` up to version 0.8 for a call to `uniroot` directly. In order to speed up things (i.e., not to call the expensive `getInfRobIC` once again at the zero, up to version 0.8 we had some awkward `assign`-`sys.frame` construction to modify the caller writing the upper inefficiency already computed to the caller environment; having capsulated this into `try` from version 0.9 on, this became even more awkward, so from version 0.9 onwards, we instead use the `TRUE`-alternative when calling it from `radiusMinimaxIC`.

Value

The inefficieny difference between the left and the right margin of a given radius interval is computed.

Methods

radius = "numeric", L2Fam = "L2ParamFamily", neighbor = "UncondNeighborhood", risk = "asMSE":

computes difference of asymptotic MSE–inefficiency for the boundaries of a given radius interval.

Author(s)

Matthias Kohl [email protected]

References

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. Submitted. 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.

`radiusMinimaxIC`, `leastFavorableRadius`