leastFavorableRadius: Generic Function for the Computation of Least Favorable Radii

In ROptEstOld: Optimally Robust Estimation - Old Version

Generic Function for the Computation of Least Favorable Radii

Description

Generic function for the computation of least favorable radii.

Usage

leastFavorableRadius(L2Fam, neighbor, risk, ...)

## S4 method for signature 'L2ParamFamily,UncondNeighborhood,asGRisk'
leastFavorableRadius(L2Fam, neighbor, risk, rho, upRad = 1, 
            z.start = NULL, A.start = NULL, upper = 100, maxiter = 100, 
            tol = .Machine$double.eps^0.4, warn = FALSE)

Arguments

L2Fam	L2-differentiable family of probability measures.
neighbor	object of class "Neighborhood".
risk	object of class "RiskType".
...	additional parameters
upRad	the upper end point of the radius interval to be searched.
rho	The considered radius interval is: [r \rho, r/\rho] with \rho\in(0,1).
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.

Value

The least favorable radius and the corresponding inefficiency are computed.

Methods

L2Fam = "L2ParamFamily", neighbor = "UncondNeighborhood", risk = "asGRisk"

computation of the least favorable radius.

Author(s)

Matthias Kohl [e-mail]

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 \Sexpr[results=rd]{tools:::Rd_expr_doi("10.18452/3638")}

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.

See Also

radiusMinimaxIC

Examples

N <- NormLocationFamily(mean=0, sd=1) 
leastFavorableRadius(L2Fam=N, neighbor=ContNeighborhood(),
                     risk=asMSE(), rho=0.5)

ROptEstOld documentation built on Feb. 4, 2024, 3 p.m.