RobLox (version 0.8.2)

rsOptIC: Computation of the optimally robust IC for AL estimators

Description

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

Usage

rsOptIC(r, mean = 0, sd = 1, bUp = 1000, delta = 1e-06, itmax = 100, 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.

delta

the desired accuracy (convergence tolerance).

itmax

the maximum number of iterations.

computeIC

logical: should IC be computed. See details below.

Value

• If 'computeIC' is 'TRUE' an object of class "ContIC" is returned, otherwise a list of Lagrange multipliers
• A
  standardizing constant
• a
  centering constant
• b
  optimal clipping bound

concept

• normal scale
• influence curve

Details

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

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 <- rsOptIC(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)