RobRex (version 1.2.0)

rgsOptIC.AL: Computation of the optimally robust IC for AL estimators

Description

The function rgsOptIC.AL computes the optimally robust IC for AL estimators in case of linear regression with unknown scale and (convex) contamination neighborhoods where the regressor is random; confer Subsubsection 7.2.1.1 of Kohl (2005).

Usage

rgsOptIC.AL(r, K, theta, scale = 1, A.rg.start, a.sc.start = 0, A.sc.start = 0.5, 
             bUp = 1000, delta = 1e-06, itmax = 50, check = FALSE)

Arguments

r

non-negative real: neighborhood radius.

K

object of class "Distribution".

theta

specified regression parameter.

scale

specified error scale.

A.rg.start

positive definite and symmetric matrix: starting value for the standardizing matrix of the regression part.

a.sc.start

real: starting value for centering constant of the scale part.

A.sc.start

positive real: starting value for the standardizing constant of the scale part.

bUp

positive real: the upper end point of the interval to be searched for b.

delta

the desired accuracy (convergence tolerance).

itmax

the maximum number of iterations.

check

logical. Should constraints be checked.

Value

Object of class "ContIC"

Details

If theta is missing, it is set to 0. If A.rg.start is missing, the inverse of the second moment matrix of K is used. The Lagrange multipliers contained in the expression of the optimally robust IC can be accessed via the accessor functions cent, clip and stand.

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

Examples

# NOT RUN {
K <- DiscreteDistribution(1:5) # = Unif({1,2,3,4,5})
IC1 <- rgsOptIC.AL(r = 0.1, K = K)
checkIC(IC1)
Risks(IC1)
cent(IC1)
clip(IC1)
stand(IC1)
# }