rlOptIC {RobLox}

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

M. Kohl (2005). Numerical Contributions to the Asymptotic Theory of Robustness. Dissertation. University of Bayreuth. https://epub.uni-bayreuth.de/id/eprint/839/2/DissMKohl.pdf.

H. Rieder (1994): Robust Asymptotic Statistics. Springer. doi:10.1007/978-1-4684-0624-5

M. Kohl, P. Ruckdeschel, and H. Rieder (2010). Infinitesimally Robust Estimation in General Smoothly Parametrized Models. Statistical Methods and Applications 19(3): 333-354. doi:10.1007/s10260-010-0133-0.

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)