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.
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, ...)
a list with items
Lagrange multiplier A
(standardizing matrix)
Lagrange multiplier a
(centering in p
-space)
Lagrange multiplier z
(centering in k
-space)
weight function involving Lagrange multipliers
(possibly modified) bias type biastype
from argument
(possibly modified) norm type normtype
from argument
(possibly modified) norm type normtype
before last (internal) update
(possibly [norm-]modified) risk risk
from argument
(possibly modified) argument std
number of iterations needed
precision achieved
used clippng height b
call with which either getLagrangeMultByIter
or
getLagrangeMultByOptim
was called
numeric; (\(>b_{\rm\scriptstyle min}\); clipping bound for which the Lagrange multipliers are searched
L2-derivative of some L2-differentiable family of probability measures.
object of class "RiskType"
.
matrix: Fisher information.
matrix: transformation of the parameter.
object of class "Neighborhood"
.
object of class "BiasType"
--- the bias type with we work.
object of class "NormType"
--- the norm type with we work.
object of class "Distribution"
.
initial value for the centering constant (in p
-space).
initial value for the centering constant (in k
-space).
initial value for the standardizing matrix.
initial value for the weight function.
matrix of (or which may coerced to) class
PosSemDefSymmMatrix
for use of different
(standardizing) norm.
logical vector: indication which components of the centering constant have to be computed.
matrix: indication which components of the standardizing matrix have to be computed.
the maximum number of iterations.
the desired accuracy (convergence tolerance).
logical: if TRUE
, some messages are printed.
logical: if TRUE
warning is issued if
maximal number of iterations is reached.
additional parameters for optim
and E
.
Peter Ruckdeschel peter.ruckdeschel@uni-oldenburg.de
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.
InfRobModel-class