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, ...)

Value

a list with items

A: Lagrange multiplier A (standardizing matrix)
a: Lagrange multiplier a (centering in p-space)
z: Lagrange multiplier z (centering in k-space)
w: weight function involving Lagrange multipliers
biastype: (possibly modified) bias type biastype from argument
normtype: (possibly modified) norm type normtype from argument
normtype.old: (possibly modified) norm type normtype before last (internal) update
risk: (possibly [norm-]modified) risk risk from argument
std: (possibly modified) argument std
iter: number of iterations needed
prec: precision achieved
b: used clippng height b
call: call with which either getLagrangeMultByIter or getLagrangeMultByOptim was called

Arguments

b: numeric; (\(>b_{\rm\scriptstyle min}\); 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 and E.

Author

Peter Ruckdeschel peter.ruckdeschel@uni-oldenburg.de

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.