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

In RobRex: Optimally Robust Influence Curves for Regression and Scale

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.

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.

Value

Object of class "ContIC"

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

Examples

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)

RobRex documentation built on Jan. 29, 2024, 3:01 a.m.