rlOptIC: Computation of the optimally robust IC for AL estimators

In RobLox: Optimally Robust Influence Curves and Estimators for Location and Scale

Computation of the optimally robust IC for AL estimators

Description

The function rlOptIC computes the optimally robust IC for AL estimators in case of normal location and (convex) contamination neighborhoods. The definition of these estimators can be found in Rieder (1994) or Kohl (2005), respectively.

Usage

rlOptIC(r, mean = 0, sd = 1, bUp = 1000, computeIC = TRUE)

Arguments

r	non-negative real: neighborhood radius.
mean	specified mean.
sd	specified standard deviation.
bUp	positive real: the upper end point of the interval to be searched for the clipping bound b.
computeIC	logical: should IC be computed. See details below.

Details

If 'computeIC' is 'FALSE' only the Lagrange multipliers 'A', 'a', and 'b' contained in the optimally robust IC are computed.

Value

If 'computeIC' is 'TRUE' an object of class "ContIC" is returned, otherwise a list of Lagrange multipliers

A	standardizing constant
a	centering constant; always '= 0' is this symmetric setup
b	optimal clipping bound

Author(s)

Matthias Kohl [e-mail]

References

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

Kohl, M. (2005) Numerical Contributions to the Asymptotic Theory of Robustness. Bayreuth: Dissertation.

See Also

ContIC-class, roblox

Examples

IC1 <- rlOptIC(r = 0.1)
distrExOptions("ErelativeTolerance" = 1e-12)
checkIC(IC1)
distrExOptions("ErelativeTolerance" = .Machine$double.eps^0.25) # default
Risks(IC1)
cent(IC1)
clip(IC1)
stand(IC1)
plot(IC1)

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