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ROptEst (version 1.0)

getInfLM: Functions to determine Lagrange multipliers

Description

Functions to determine Lagrange multipliers A and a in a Hampel problem or in a(n) (inner) loop in a MSE problem; can be done either by optimization or by fixed point iteration. These functions are rarely called directly.

Usage

getLagrangeMultByIter(b, L2deriv, risk, trafo, neighbor, biastype, normtype, Distr, a.start, z.start, A.start, w.start, std, z.comp, A.comp, maxiter, tol, verbose = NULL, warnit = TRUE)
getLagrangeMultByOptim(b, L2deriv, risk, FI, trafo, neighbor, biastype, normtype, Distr, a.start, z.start, A.start, w.start,  std, z.comp, A.comp, maxiter, tol, verbose = NULL, ...)

Arguments

b
numeric; ($>b_min$; clipping bound for which the Lagrange multipliers are searched
L2deriv
L2-derivative of some L2-differentiable family of probability measures.
risk
object of class "RiskType".
FI
matrix: Fisher information.
trafo
matrix: transformation of the parameter.
neighbor
object of class "Neighborhood".
biastype
object of class "BiasType" --- the bias type with we work.
normtype
object of class "NormType" --- the norm type with we work.
Distr
object of class "Distribution".
a.start
initial value for the centering constant (in p-space).
z.start
initial value for the centering constant (in k-space).
A.start
initial value for the standardizing matrix.
w.start
initial value for the weight function.
std
matrix of (or which may coerced to) class PosSemDefSymmMatrix for use of different (standardizing) norm.
z.comp
logical vector: indication which components of the centering constant have to be computed.
A.comp
matrix: indication which components of the standardizing matrix have to be computed.
maxiter
the maximum number of iterations.
tol
the desired accuracy (convergence tolerance).
verbose
logical: if TRUE, some messages are printed.
warnit
logical: if TRUE warning is issued if maximal number of iterations is reached.
...
additional parameters for optim.

Value

References

Rieder, H. (1980) Estimates derived from robust tests. Ann. Stats. 8: 106-115.

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

Ruckdeschel, P. and Rieder, H. (2004) Optimal Influence Curves for General Loss Functions. Statistics & Decisions 22: 201-223.

Ruckdeschel, P. (2005) Optimally One-Sided Bounded Influence Curves. Mathematical Methods in Statistics 14(1), 105-131.

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

See Also

InfRobModel-class